When a point is constructed on a path, you can animate the point along the path, either by choosing Display | Animate or by creating an Animation button.

To animate an independent point along a path, you must first merge the point to the path.

If the intended locus driver is a point on a path, the path is automatically used as the domain for the driver.

Select the driver and the driven object. Then choose Construct | Locus.

If the intended locus driver is an independent point, you must select the path to use it as the domain.

Select the driver, the path, and the driven object. Then choose Construct | Locus.

When you construct a path coinciding with, or collinear to, a longer path (for example, when you construct an arc on the circumference of a circle, or when you construct a segment along a line), the longer path becomes dashed to better display the shorter path coinciding with it.

Since a dashed coordinate axis is seldom desirable, a straight object constructed on an axis is drawn one step thicker than the default line thickness.

Use Sketchpad’s built-in transformations to create a transformed image of a path.

Select the picture and choose Translate, Rotate, Reflect, or Dilate from the Transform menu. Depending on the transformation you want, you may need to mark various objects or values to serve as center, distance, angle, ratio, or mirror.

These four transformations, and any transformation that combines them, are called similarity transformations because the transformed image is similar to the original: angles and ratios of distances are preserved.

Use Sketchpad’s custom transformations to create an arbitrary transformed image of a path.

Use two points, one of which depends on the other, to define a custom transformation.

Select the path you want to transform.

Choose the custom transformation from the bottom of the Transform menu.

If the two points that define the custom transformation are related using only Sketchpad’s built-in transformations, the result is a normal transformed path, just as if you had applied the various transformations directly to the original path.

If the pre-image path is a segment, the image remains a segment; if the pre-image is a circle, so is the image.

If the two points that define the custom transformation are related in some other way, the result is a sampled transformed path.

Such transformed images must be displayed using a sampling process: The transformed path is displayed by sampling locations along the pre-image and then transforming each sample to create the transformed image. The smoothness and level of detail of the transformed path depend on the number of samples used. To change the number of samples and whether the transformed path is displayed as continuous or discrete, select the transformed path and choose Edit | Properties | Plot.

When polygons and other interiors are transformed in this way, only the border of the interior is transformed.