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 Δ[i]ABC[/i] in the first quadrant where its vertices are on the grid. measure the coordinates of each vertex and record it below. [br][br]A = ______ B = ______ C = ______
2. Make a prediction where the image of Δ[i]ABC[/i] would lie once rotated 90[b]°[/b] about the origin. [br][br][i][i]Rotated 90[b]°[/b] about the origin[b] prediction[/b][/i][/i]: A′ = ______ B′ = ______ C′ = ______[br][br]Then rotate Δ[i]ABC 90[b]°[/b] about the origin[/i] to assess your prediction. Record your results below.[br][br][i]Rotated 90[b]°[/b] about the origin[b] actual[/b][/i]: A′ = ______ B′ =______ C′ = _______[br][br][br]
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[b]°[/b]. 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[b]°[/b].
4. Make a prediction where the image of Δ[i]ABC[/i] would lie once rotated 180[b]°[/b] about the origin. [br][br][i][i]Rotated 180[b]°[/b] about the origin[b] prediction[/b][/i][/i]: A′ = ______ B′ = ______ C′ = ______[br][br]Then rotate Δ[i]ABC 180[b]°[/b] about the origin[/i] to assess your prediction. Record your results below.[br][br][i]Rotated 180[b]°[/b] about the origin[b] actual[/b][/i]: A′ = ______ B′ =______ C′ = _______[br][br][br]
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[b]°[/b]. 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[b]°[/b].
6. Make a prediction where the image of Δ[i]ABC[/i] would lie once rotated 270[b]°[/b] about the origin. [br][br][i][i]Rotated 270[b]°[/b] about the origin[b] prediction[/b][/i][/i]: A′ = ______ B′ = ______ C′ = ______[br][br]Then rotate Δ[i]ABC 270[b]°[/b] about the origin[/i] to assess your prediction. Record your results below.[br][br][i]Rotated 270[b]°[/b] about the origin[b] actual[/b][/i]: A′ = ______ B′ =______ C′ = _______[br][br][br]
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[b]°[/b]. 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[b]°[/b].
8. Make some overall general statements about rotations.