# ROTATIONS IN THE COORDINATE PLANE

- Author:
- Suzanne Harper

1. Construct Δ*ABC* in the first quadrant where its vertices are on the grid. measure the coordinates of each vertex and record it below.
A = ______ B = ______ C = ______

2. Make a prediction where the image of Δ*ABC* would lie once rotated 90**°** about the origin.
* Rotated 90° about the origin prediction*: A′ = ______ B′ = ______ C′ = ______
Then rotate Δ

*ABC 90*to assess your prediction. Record your results below.

**°**about the origin*Rotated 90*: A′ = ______ B′ =______ C′ = _______

**°**about the origin**actual**3. Drag the vertices to different locations on the grid and look for a relationship between a point’s coordinates and the coordinates of the rotated image about the origin by 90**°**. Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of the rotated image about the origin by 90**°**.

4. Make a prediction where the image of Δ*ABC* would lie once rotated 180**°** about the origin.
* Rotated 180° about the origin prediction*: A′ = ______ B′ = ______ C′ = ______
Then rotate Δ

*ABC 180*to assess your prediction. Record your results below.

**°**about the origin*Rotated 180*: A′ = ______ B′ =______ C′ = _______

**°**about the origin**actual**5. Drag the vertices to different locations on the grid and look for a relationship between a point’s coordinates and the coordinates of the rotated image about the origin by 180**°**. Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of the rotated image about the origin by 180**°**.

6. Make a prediction where the image of Δ*ABC* would lie once rotated 270**°** about the origin.
* Rotated 270° about the origin prediction*: A′ = ______ B′ = ______ C′ = ______
Then rotate Δ

*ABC 270*to assess your prediction. Record your results below.

**°**about the origin*Rotated 270*: A′ = ______ B′ =______ C′ = _______

**°**about the origin**actual**7. Drag the vertices to different locations on the grid and look for a relationship between a point’s coordinates and the coordinates of the rotated image about the origin by 270**°**. Describe any relationship you observe between the coordinates of the vertices of your original triangle and the coordinates of the rotated image about the origin by 270**°**.

8. Make some overall general statements about rotations.