Transformations Worksheet: Translate, Rotate & Reflect
Goal: Apply translations, rotations and reflections to a triangle on the coordinate plane, write the coordinate rule for each, and see which transformations keep the size the same.
What to do
- Open the transformation playground. The original triangle is A(−2, −1), B(2, −1), C(0, 2), with an area of 6 square units.
- Press “Translate”, set “Horizontal translation” to 2 and “Vertical translation” to 1, and record A′, B′, C′ and the new area.
- Press “Rotate” and record the results for “Rotation angle (°)” = 90, then 180.
- Record the results for “Reflect over x-axis” and “Reflect over y-axis”. Then press “Scale from origin”, set “Scale factor” to 2, and record.
Record your results
| Setting | A′ | B′ | C′ | New area |
|---|---|---|---|---|
| Translate by (2, 1) | ||||
| Rotate 90° | ||||
| Rotate 180° | ||||
| Reflect over x-axis | ||||
| Reflect over y-axis | ||||
| Scale factor 2 |
Questions
Write the coordinate rule for the translation you used. Did the area change?
Look at the 90° rotation. Find the rule that turns each original point into its image.
Compare the 180° rotation with two reflections in a row: first over the x-axis, then over the y-axis. What do you find?
Which transformations kept the area at 6 square units? Which one changed it, and by what factor?
Predict where C(0, 2) lands after a 270° counterclockwise rotation. Then set the rotation angle to 270 to check.
In the original triangle, going A → B → C runs counterclockwise. Which transformations in your table reverse this to clockwise?
Free from Geometry Lab · geometrylab.net · 8.G.A.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates. HSG-CO.A.5: Given a geometric figure and a rotation, reflection or translation, draw the transformed figure.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.