# ROTATIONS IN THE COORDINATE PLANE

In this part of the exploration, you’ll investigate the effect of the coordinates of points when you rotate them 90°, 180°, and 270° in the coordinate plane.

1. Construct ΔABC 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 ΔABC would lie once rotated 90° about the origin. Rotated 90° about the origin prediction:        A′ = ______  B′ = ______ C′ = ______ Then rotate ΔABC 90° about the origin to assess your prediction. Record your results below. Rotated 90° about the origin actual:              A′ = ______  B′ =______ C′ = _______

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 ΔABC would lie once rotated 180° about the origin. Rotated 180° about the origin prediction:        A′ = ______  B′ = ______ C′ = ______ Then rotate ΔABC 180° about the origin to assess your prediction. Record your results below. Rotated 180° about the origin actual:              A′ = ______  B′ =______ C′ = _______

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 ΔABC would lie once rotated 270° about the origin. Rotated 270° about the origin prediction:        A′ = ______  B′ = ______ C′ = ______ Then rotate ΔABC 270° about the origin to assess your prediction. Record your results below. Rotated 270° about the origin actual:              A′ = ______  B′ =______ C′ = _______

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.