Illustrator provides tools for 5 basic types of transformations:
Moving,
Scaling,
Rotating,
Reflecting (aka mirroring),
Shearing.
The tools allow you to do the 5 operations visually, but Illustrator also provides useful quantitative methods that allow you to do the transformations by means of a dialog box:
Quantitative Methods
The quantitative methods include the:
Tool dialog box, which you access by, selecting the shape, and then selecting one of the transformation tools, and then pressing the Enter key; or simply by selecting the shape and then double-clicking one of the 5 tools.
Transformation panel, which you can find included in the Properties panel, or via Windows > Transform.
The above methods are fast and convenient, but they are destructive, i.e., they permanently alter the object's anchor points and control handles. Therefore, once you save and exit the document, the original structure of the Object is destroyed, so that you cannot start over. In contrast, you could use the Effect > Distort & Transform > Transform dialog, which is non-destructive. The dialog makes it easy to work iteratively, because transformed objects remain modifiable, reversible, and the original paths remain editable.
Tool Dialog
Each tool has its own dialog box that allows you to exactly specify fields that define the transformation. Not only is this method precise, but it tells you exactly how the transformation works. In addition, all the tool dialogs allow you to, not only make the transformation, but also make a copy of the transformed shape.
The method of accessing the dialog box is similar for all 5 transformations:
Select the object.
Go to the tool associated with the transformation and either:
Double click the tool, or
Select the tool and press the Enter key.
Enter the parameters (options) for the transformation.
Click OK to implement the transformation, or click the Copy button to make a copy of the transformed version of the object and leave the original object in its original location, unchanged.
Transform Panel
The Windows > Transform panel (Shift + F8) has a general area, which is the same regardless of the object selected, and an area specifically for Live Shapes, which displays content only if the selected object is a Live Shape and then the Transformation panel will include a section that is devoted specifically to the transformations that apply to that type of shape.
The general Transformation panel fields allow you to:
Move a shape by updating the X and Y coordinates of the center of the object's bounding box. To see the center of an object that is not a Live Shape: select the shape, then open the Window > Attributes panel and select the Show Center icon, .
Scale a shape by updating its height (H) and width (W) fields.
Set a Reference Point for rotations or reflections .
Rotate a shape, relative to the reference point, by updating the angle of rotation field .
Reflect a shape horizontally or vertically, relative to the reference point, by selecting one of the "Flip" icons .
Hint
When you have selected a target object, you can find both the general and the specific Transformation panel fields included in the Windows > Properties panel. However, the Transformation control in the Control panel includes only the general fields.
Visual Method
The role of the Reference Point in Transformations
The visual methods use one of the transformation tools in Illustrator's Basic Toolbar.
Move tool (i.e., the Selection tool)
Rotate tool
Reflect tool
Scale tool
Shearing tool
Except for the move operation, the transformations take place relative to a fixed Reference point (or a line, in the case of reflection), and the tools work in a roughly similar way:
Select the object or objects.
Single-click to invoke the tool (double-clicking displays the tool menu). Ai changes the cursor to a cross-hair.
Click with the cross hair to set a Reference point (the Reflect Tool can use two points to reflect relative to a line). Ai changes to a Selection cursor.
Click and drag to transform the selected objects relative to the Reference point. The Reference point remains fixed, and in the transformation process, the other points move relative to it.
The organization and much of the content of this article follows that of the Transforming and Positioning Art section of Mordy Golding's 2010 Lynda.com course, Illustrator CS5 Essential Training.
Moving
There are several direct and indirect ways to move selected objects:
Nudge an Object. Move an object in small increments to fine-tune a placement.
Move and Copy Operations. The standard operations (quantitative and visual) for moving an object allow you to both move and copy that object.
Move with the Windows > Transform panel. This panel has been enhanced so that not only can it move, rotate or shear an object, but when used on Live Shapes, it acts as a Swiss Army knife that can modify any of the defining properties of any of the Live Shape tools. For example, working with a rectangle, the panel can modify the width, height or corner properties; working with a ellipse, the panel can modify the pie angle, etc.
Align and Distribute a Selection of Objects, which is the subject of a separate article.
Nudge an Object
To move an object by small increments, i.e., to nudge it into place in Adobe Illustrator:
Optionally, set the Keyboard Increment in the preferences panel (Edit > Preferences> General, or Ctrl + k).
Select the art.
Tap an arrow key.
Moving and Copying Operations
The basic, most used, move operations allow you to both move and copy an object.
Move or Copy via the Move Dialog
Setting the precise displacement with the Horizontal and Vertical fields in the Move dialog
The Move dialog allows you to move an object either by specifying: (A) a horizontal or vertical displacement, or (B) by specifying a displacement distance and an angle of displacement.
To move or copy an object quantitatively, via the Move dialog box, in Adobe Illustrator:
Select the Object.
Go to the Selection tool and either:
Double click the tool, or
Select the tool and press the Enter key.
Specify the positioning parameters.
Check the Preview checkbox to see the effect of the change.
Click Copy to create a new copy in the specified position, or OK to just move the object.
Move or Copy Visually with the Selection Tool
To move or copy an object with the Select tool in Adobe Illustrator:
Select the object or objects that you want to move or copy.
Drag with the Selection tool to just move the objects, Alt + drag to copy the objects.
Hint
Shift + drag or Shift + Alt + drag constrains the move or copy operation to move horizontally, vertically, or along a 45 or 135-degree angle.
Repeat a Move or Copy Operation
When you move or copy an object, Ai automatically remembers the parameters.
In Adobe Illustrator, to repeat a copy or move operation that you have just finished performing, simply :
Execute the command sequence Object > Transform > Transform Again (Ctrl + d).
Move with the Transform Panel
Setting the precise displacement with the X and Y fields of the Transform panel.
To move an object using the Transformation panel in Adobe Illustrator:
Select the Object.
Go to the Window > Transform panel.
Update the X and Y coordinates.
Press the Enter key. Ai will move the shape to the specified location.
Rotation
You can rotate a selection precisely with two quantitative methods (the Rotation Dialog or the Transformation panel, or you can work visually with the Rotation tool.
Rotate Quantitatively with the Rotate Tool Dialog
Visual explanation of the Rotate dialog options.
To rotate an object (or objects) using the Rotate tool dialog box settings in Adobe Illustrator:
Select the Objects.
Go to the Rotation tool and either:
Double click the tool, or
Select the tool and press the Enter key.
Specify the rotation angle. Ai will rotate the object around the Reference point, which by default is at the center of the selected object or objects.
If the object has a pattern fill, choose one of the buttons in the Options row to specify whether you want to rotate the object only, the pattern only, or both the pattern and the object together (the default).
Check the Preview checkbox to see the effect of the change.
Click Copy to create a new copy in the specified position, or click OK to just rotate the object counterclockwise through the specified angle.
Hint
The Rotate tool dialog box (unlike the Transform panel) does not provide a field to set the Reference point. Ai simply places a default Reference point at the center of the Bounding Area (the area that would be covered by the Bounding Box if it were turned on). Of course, it is not necessary to have Bounding Boxes enabled, but it is worth keeping in mind that Ai uses the Bounding Area as a frame of reference. Therefore, the center about which an object rotates will be, not the center of the object, but the center of the Bounding Box.
You can both set the Reference Point and pop up the Rotate Dialog in one operation. Simply single click the Rotate tool to activate it, select the object to be rotated, and then Alt + click. Ai will set the Reference Point and pop up the Rotate dialog box.
Rotate with the Transform Panel
Use the Transform Panel to set a fixed Reference Point and rotate the object around it
Using the Transform panel to rotate objects has the advantage that you can use the small, square 3 x 3 array of buttons (at the upper left of the panel) to set the Reference Point, i.e., the fixed point about which you want the object to rotate.
To use the Transform panel to rotate an object in Adobe Illustrator:
Select the Object.
Go to the Window > Transform panel.
Select the Reference Point about which you want the object to rotate.
If the object has a pattern fill, open the Transform panel's Options dropdown list by clicking on the hamburger button in the upper right corner. Choose whether you want to rotate the object only, the pattern only, or both.
Specify the rotation angle.
Press the Enter key. Ai will rotate the object counterclockwise through the specified angle.
Rotating with the Rotate Tool
The Rotate tool has the advantage that you can set the Reference point (about which you want to rotate the object) visually and set it anywhere on the artboard, even outside of the object that you rotate.
To use the Rotate tool to rotate an object in Adobe Illustrator:
Select the object or objects that you want to rotate.
Click the Rotate tool (shortcut is the r-key). Ai will change the cursor to a cross-hair.
Click once with the cross-hair to fix the Reference point, i.e., the point around which the object will rotate.
Ai will change the cursor to one that looks like the Selection tool's black arrow.
With the black arrow, click and drag to rotate the object.
As you drag, Ai will rotate the object about the Reference point.
Hint
You can both set the Reference Point visually (anywhere on the Artboard), and use the Rotate dialog to precisely set the angle of rotation. Simply, Alt + click to set the reference point. Ai will both (a) set the Reference Point and (b) pop up the Rotate Dialog.
Reflection
A reflection is a transformation of an object relative to a line, called the axis of reflection. The transformation moves or copies each point of the object to another point that is the same distance from the axis line, but on the other side. The reflection operation creates a mirror image of the reflected object or a figure with bilateral symmetry. The line of reflection is analogous to the mirror. There are two common ways to reflect objects:
The Dialog has the advantage that it allows you to precisely control the angle of the axis of reflection, but the dialog imposes the limitation that the axis line must pass through the center of the box that contains the object. By contrast, the Reflection tool does not allow you to precisely control the angle of the axis of reflection, but it does allow you to specify a true axis of reflection, which need not even pass through the object.
Reflect an Object with the Reflection Dialog
Reflecting an object relative to a precisely specified axis using the Reflect dialog.
To reflect an object using the Reflect tool's dialog box in Adobe Illustrator:
Select the object.
Go to the Reflect tool and either:
Double click the tool, or
Select the tool and press the Enter key.
Specify the rotation angle.
If the object has a pattern fill, choose one of the buttons in the Options row to specify whether you want to rotate the object only, the pattern only, or both the pattern and the object together (the default).
Check the Preview checkbox to see the effect of the change.
Click Copy to create a new copy in the specified position, or click OK to just rotate the object counterclockwise through the specified angle.
Reflect an Object with the Reflect Tool
To specify an axis of reflection and reflect an object relative to the axis in Adobe Illustrator:
Select the object.
Click the Reflect tool (under the Rotate tool).
Define the reflection axis by specifying two points:
Click on the first point that you want to be the reflection axis line. The cursor will change to a pointer.
Then either click, or Alt + click to create the second point. Ai will create the reflection as soon as you click the second time. If you simply click, AI will just reflect the object. If you Alt + Click, Ai will create a copy as soon as you make the second click.
How to use Reflection and Copying to draw a bilaterally symmetrical figure.
Hint
Reflecting, with copying is often used to complete a symmetrical figure from a drawing of one half of it. To complete the missing half of a symmetric figure:
Select the completed half.
Get the Reflect tool. Ai will change the cursor to a cross-hair to set the Reference point.
With the cross-hair, click the bottom anchor point on the open side of the figure to make it the Reference point. Ai will change the cursor to the Selection tool.
Constraining the proportions via Shift key and creating a copy via Alt key, Alt + Shift + Click on the top anchor point to create the mirror image part of the figure. The reflection process will create overlapping duplicate anchor points on the axis of reflection where you placed the Reference Points.
To combine the two halves, marquee-select around one of the Reference Points and execute the Object > Path > Join (Ctrl + j) command.
Scaling
The phrase "scaling a figure" usually refers to uniform scaling, i.e., creating a similar figure in which the angles remain unchanged. However, Ai's Scale tool, and its Dialog box, can do not just uniform scaling but also non-uniform scaling, in which you can expand or contract the horizontal, and vertical dimensions independently. The tool and the dialog box are the main ways of doing scaling. The Transform panel can do scaling, but not by a scaling factor, but only by changing the absolute width and height values. In contrast, the Effect > Distort & Transform > Transform Effect can do percentage scaling in both the horizontal and vertical dimensions independently.
Scaling with the Scale Tool Dialog
Illustration of using the Scale tool dialog.
The Scale dialog allows you to multiply the dimensions of a selected object by a percentage factor times its current value (i.e., a scaling factor of 100% causes no change). By checking the Scale Corners or the Scale Strokes and Effects checkboxes, you can also tell the dialog to proportionally scale the target object's corners, or its Strokes and Effects
To scale an object or objects quantitatively using the Scale dialog box settings in Adobe Illustrator:
Select the Object.
Go to the Scale tool and either:
Double click the tool, or
Select the tool and press the Enter key.
Select a radio button for either uniform or non-uniform scaling.
Enter the scaling percentage or percentages: a single value for uniform scaling or both a horizontal and a vertical value for non-uniform scaling.
Optionally, use the checkboxes the tell Illustrator if you want it to scale the corners or scale the strokes and effects (or both), without which the scaled figure can look decidedly weird.
Check the Preview checkbox to see the effect of the change.
Either click Copy to create a new copy in the specified position, or click OK to just scale the object.
Scaling with the Scale Tool
Example of using the Scale tool to set an off-center Reference Point and then dragging to produce non-uniform scaling.
To scale an object or objects using the Scale tool in Adobe Illustrator:
Select the object or objects to be scaled.
Get the Scale tool.
Click once to fix the Reference point, i.e., the point from which the object will scale. Ai will change the cursor to the Selection tool.
Click + Drag to scale the object's dimensions independently, Shift + Click + Drag to scale proportionally, or Alt + Click + Drag to create a scaled copy of the original object.
Shearing
Example showing a horizontal Shear Axis, the line perpendicular to the Shear Axis, and a Shear Angle of 45 degrees.
A horizontal shearing transformation will push all the points of a figure along the horizontal axis in such a way that all lines that are perpendicular to the horizontal axis slant away from the perpendicular at the same (specified) angle. So, if the figure is a rectangle; the transformation will push it over onto its side and make it into a parallelogram.
In Illustrator, not all shearing transformations need to push along the horizontal axis. In general, the direction along which the shearing transformation pushes is called the Shearing Axis and the amount of slant from the perpendicular is called the Shearing Angle. In Illustrator, you can set the Shearing Axis, the Shearing Angle, and a Shearing Reference Point (i.e., a point that remains fixed and will not be displaced by the transformation).
The Shear transformation measures the amount that it must push each point in the figure from two lines: (A) a line that is perpendicular to the Shear Axis and (B) a Shearing Angle line, which is slanted at the Shear Angle and that intersects the perpendicular at the level of the reference point. The amount and direction that Ai pushes each point is proportional to the distance that the Shearing Angle line is from the perpendicular line at that point on the perpendicular.
Shearing relative to a Reference Point in the lower left corner. The Shearing transformation pushes the point at the base of the arrow to the point at its tip.Shearing relative to a Reference Point located in the center. The Shearing transformation pushes the point at the base of the arrow to the point at its tip.
Shear with the Shear Dialog
Setting the Shear Angle (the angle of slant) and the angle of the Shear Axis (the angle of push) in the Shear Dialog
To Shear a figure quantitatively with the Shear dialog box in Adobe Illustrator:
Select the objects that you want to Shear.
Optionally, if you want to set the Reference point to a place other than the center of the selection, get the Shear tool and Alt + Click inside the selection. Ai will mark the point as the Reference point and launch the Shear dialog box.
Double-click the Shear tool. Ai will open the Shear Dialog box.
In the dialog, set the Shear Angle, the degree of slant. Ai measures the Shear Angle from the perpendicular line, in the clockwise direction.
Set the Shear Axis (which Ai measures in the counterclockwise direction from the bottom of the Artboard) in one of three ways:
Click the Horizontal radio button. Ai will set the Shear Axis (the direction along which Ai will push all the points to 0. The perpendicular will then be vertical.
Click the Vertical radio button. Ai will set the Shear Axis (the direction along which Ai will push all the points to 90 degrees. The perpendicular will then be horizontal.
Click the Angle radio button and set the Shear Axis to an arbitrary angle (x). The perpendicular will then be x + 90 degrees.
Click the OK or the Copy button.
Shear with the Shearing Tool
To shear and copy an object or objects using the Shearing tool in Adobe Illustrator:
Select the object (or objects).
Get the Shear tool (under the Scale tool).
Click once inside the selection to position the Reference Point i.e., the point that will remain invariant during the shearing operation.
Drag the cursor to shear the object or Alt + Drag to make a copy of the sheared object. Ai will perform the shearing operation in which the Reference point will remain unchanged and the Bounding Area will slant in the direction in which you dragged the cursor. That is, the direction in which you drag is the Shearing Axis.
Bounding Box
The bounding box provides an easy way to do rotation and scaling transformations, and it is also important for understanding several tool-based transformations.
Any selected object or selection of objects has an invisible bounding area, a rectangular region that encloses the selection. In most transformations, the bounding area acts as a framework that defines the transformation's scope and geometry. For example, the locations shown on the Reference point locater in the Transform panel defines the point of Reference for transformations relative to the bounding area.
Bounding Box Controls
You can make the bounding area visible by executing the command: View > Show Bounding Box (Shift + Ctrl + B). As shown in the accompanying figure, the Bounding Box has 4 side controls and 4 corner controls.
In addition, related to (but a bit different from the 8 bounding box controls) there are active areas, each of which Ai identifies with a distinctive cursor, from which you can initiate a move, rotation, stretching, or compression transformation.
Using-the-Bounding Box
To use the Bounding Box areas to make transformations in Adobe Illustrator, you must both place your cursor in a specific location and execute a specific gesture, as described below:
With the cursor inside the Bounding Box (which Ai identifies by a rectangular cursor with a modifier that looks like a miniature Bounding Box), dragging the cursor will simply move the selected object, just as it would without the bounding box.
Bounding Box Scale Gesture
With the cursor on a Corner control (which Ai identifies by a cursor with a diagonal double-headed arrow) dragging the cursor will move the corner of the Bounding Box and stretch or compress the selection horizontally and vertically, while the opposite corner will remain fixed.
Bounding Box Rotate Gesture
With the cursor in a small area just outside a corner control (which Ai, identifies by a cursor with a bent, double-headed arrow) dragging the cursor will rotate the selected object.
With the cursor on a Side control, which Ai identifies by a cursor with a horizontal, double-headed arrow, dragging the cursor will stretch or compress the selected object, while the opposite side will remain fixed.
Bounding Box Stretch Gesture
Results of Bounding Box Modifier Key Constraints on Scaling and Rotation
Bounding Box Modifier Keys
Illustrator provides two modifier keys that constrain the stretching, and compression of the Bounding Box and its content:
Used with the Bounding Box, the Shift-key constrains the result of rotation, stretching, and compression. When dragging the bent arrow cursor to perform rotation, the Shift-key constrains the rotation to angles that are multiples of 45 degrees. When dragging a corner or a side, the Shift-key constrains the result to scaling that preserves the aspect ratio of the Bounding Box, i.e., the scaled figure is always directly proportional (geometrically similar) to the original.
The Alt-key makes Ai scale the Bounding Box from the center. That is, when scaling by dragging a corner, Ai moves the corner and its opposite corner, but the center remains fixed. Similarly, when scaling by dragging a side, both sides move, but the center remains fixed.
Free Transform Tool
The Free Transform tool allows you to scale, skew, rotate, or distort a figure relative to a special bounding box.
Using the Free Transform Tool
To visually transform a figure with the Free Transform tool in Adobe Illustrator:
Activate the tool on an object:
Select the object that you want to transform.
The Free Transform tool's bounding box.
Get the Free Transform tool (e-key). Ai will surround the figure with a bounding box that has unfilled control points. The bounding box is unique to the tool; it is not the bounding box that you get by executing the View > Show Bounding Box command. The tool's bounding box provides unfilled side and corner points that you can grab to visually transform the figure. The unfilled control points become important when you want to hover over a point to target it so that you can begin a transformation relative to that point. Ai signals that you have successfully targeted the point by changing the unfilled point to a filled point.
The result of using the tool depends upon: (A) What bounding box point you target, (B) What modifier keys you press, and (C) How you drag with the mouse. Take one of the following actions:
Scale in Both Dimensions
To Scalea selected figurealong both dimensions: Hover over a corner point on the bounding box. Ai will switch to an x-shaped cursor that is made up of a curved arrow that is crossed by a straight arrow (). Depress the left mouse button, and reposition the cursor slightly until you see that Ai has filled the point. Then drag the corner toward the opposite corner. Shift + Click + Drag constrains the scaling to be proportional.
Scale in One Dimension
To Scalea selected figure along only one dimension. Hover over a side point on the bounding box. Ai will switch to a plus-shaped (+), double-arrow cursor (). Depress the left mouse button, and reposition the cursor slightly until you see that Ai has filled the point. Then drag the point perpendicular to the side.
Skew by Dragging a Side Point along the Shearing Axis
To Skew a selected figure: Hover over a side point on the bounding box. Ai will switch to a plus-shaped (+), double-arrow cursor (). Depress the left mouse button, and reposition it slightly until you see that Ai has filled the point. Then drag the point parallel to the side and in the direction toward which you want the figure to skew.
Rotate by Dragging the Free Transform tool's Curved Arrow cursor around a Corner Point
To Rotatea selected figure: Hover outside a corner until you see Ai switch to a cursor that is shaped like a curved double-arrow (). Then Drag around the object.
Distort a figure from a Corner Point using the Free Transform tool.
To Distort a selected figure by moving a corner point: Hover over the corner point. Ai will switch to an x-shaped cursor that is made up of a curved arrow that is crossed by a straight arrow (). Depress the left mouse button. When you see that Ai has filled the point, press the Ctrl-key and drag toward or away from the opposite corner.
Give a figure a Perspective Distortion by dragging a Corner Point with the Shift, Ctrl, and Alt modifier keys depressed.
To Perspective Distort a selected figure from a bounding box corner point: Hover over the point. Ai will switch to an x-shaped cursor that is made up of a curved arrow that is crossed by a straight arrow (). Depress the left mouse button. When you see that Ai has filled the corner point, press the Ctrl-key + the Shift-key + the Alt-key and drag the corner in a direction that is parallel to one of the dimensions of the bounding box.
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allows you to scale, skew, rotate, or distort a figure relative to a special bounding box.
). Depress the left mouse button, and reposition the cursor slightly until you see that Ai has filled the point. Then drag the corner toward the opposite corner. Shift + Click + Drag constrains the scaling to be proportional.
). Depress the left mouse button, and reposition the cursor slightly until you see that Ai has filled the point. Then drag the point perpendicular to the side. 
). Then Drag around the object.
