Geometry Transformations Worksheet Generator

About this tool

Transformations ask students to move a figure on the coordinate plane and say exactly where it lands. The practice that sticks combines two skills: drawing the image, and describing it with coordinates. Each problem on these worksheets asks for both.

You can focus on one idea at a time with translations, reflections, rotations about the origin, or dilations from the origin. Mixed sheets give one of each. Two-step problems ask students to compose, for example, a reflection followed by a translation, which is where order starts to matter.

Every figure is built so that the image stays on the grid. Dilations that shrink a figure only use even coordinates so the answers are whole numbers. Behind the scenes, each answer is recomputed a second way with matrices, and each result is checked against what the transformation should preserve: side lengths for rigid motions, orientation for reflections, and area scaled by the square of the scale factor for dilations.

How to use it

1. Pick the transformation type. For a first pass at a topic, choose a single type. Use Mixed to review.
2. Choose easier for reflections over the axes, small translations, and 90 or 180 degree rotations. Harder adds the lines y = x and y = −x, bigger shifts and more scale factors.
3. Print the worksheet. Students plot the image, connect the vertices and write each new coordinate pair.
4. The answer key draws the original in blue, the image in red, and any middle step as a dashed outline, then lists the rule.

The rules, in one place

A reflection over the x-axis turns (x, y) into (x, −y). Over the y-axis it gives (−x, y). Over y = x the coordinates swap, so (x, y) becomes (y, x). A 90 degree counterclockwise rotation about the origin turns (x, y) into (−y, x), and a 180 degree rotation gives (−x, −y). A dilation from the origin with scale factor k multiplies both coordinates by k.

Translations, reflections and rotations are rigid motions. They keep side lengths and angles the same. Dilations keep angles but change side lengths, so the image is similar to the original, not congruent.