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This Transform menu command constructs a dilated image of the selected geometric object(s).

In a dilated image, a designated ratio is used to move every point of the original closer to or farther away from the center point. If the ratio is greater than 1, the image points are farther away from the center than the originals and the image is larger than the original image. If the ratio is less than 1, the image points are nearer to the center and the image is smaller.

Sketchpad has both a Dilate Arrow tool and a Dilate command. When you use the tool, you dilate the original object. When you use the command, you create a new object — a dilated image of the original object.


You can dilate points, straight objects, circles, arcs, interiors, and pictures. You cannot dilate iterated images, and you cannot apply the Dilate command to loci, function plots, and other sampled objects. (However, you can use a custom transformation to dilate point loci, function plots, parametric plots, and sampled transformed paths.)

Before choosing this command, you may want to mark a center point and mark a ratio or scale factor.

Mark a center point by double-clicking with the Arrow tool. If you dilate without first marking a center, Sketchpad will mark one for you.

1.Select the object(s) you want to dilate.

2.Choose Transform | Dilate. The Dilate dialog box appears, and a dilated image of your selections appears in the sketch.

3.Choose either Fixed Ratio or Marked Ratio, as described below.

4.Click a point in the sketch to change the marked center, click a measurement with no units to set the marked scale factor, or click two segments to set the marked segment ratio.

5.When you have chosen the options you want and entered any required values, click Dilate.

The dilated image appears.

Dilate by Fixed Ratio

Choose Fixed Ratio to designate a fixed ratio by entering both a numerator and a denominator. A ratio smaller than 1 results in an image that’s smaller than the original, and a ratio greater than 1 results in an image that’s larger.

Dilate by Marked Ratio

Choose Marked Ratio to dilate your selection based on a marked ratio or scale factor you’ve specified using the Transform | Mark Ratio command. This choice is disabled if you haven’t already marked a ratio. However, if you want to use a ratio of two segments that exist in your sketch, click the segments now to mark them. Similarly, if you want to use a scale factor that exists in your sketch, click it now to mark it.