How can you tell by looking at the coordinates of the two triangles that Δ A’B’C’ is a 180° rotation of Δ ABC?
A The coordinates cannot prove a 180° rotation.
B The y-coordinates of the points on Δ A’A’B’C’ have opposite signs from the corresponding points on Δ ABC.
C The x-coordinates of the points on Δ A’A’B’C’ have opposite signs from the corresponding points on Δ ABC.
D Both the x and y coordinates of the points on Δ A’A’B’C’ have opposite signs from the corresponding points on Δ ABC.
How can you tell by looking at the coordinates of the two triangles that Δ A’B’C’ is a 180° rotation of Δ ABC?
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The correct answer is: D Both the x and y coordinates of the points on Δ A’A’B’C’ have opposite signs from the corresponding points on Δ ABC.
Explanation: A 180° rotation around the origin transforms a point (x, y) to (-x, -y). This means that both the x and y coordinates will change to their opposite signs. If you observe that the coordinates of triangles A’B’C’ show this relationship to A B C, it confirms a 180° rotation.