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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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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?

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.




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    1. Quizzma Team

      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 will result in each point (x, y) being transformed into (-x, -y). This means that both the x-coordinates and the y-coordinates will change to their opposite values. Therefore, if you see that each point on triangle A’B’C’ has both x and y coordinates that have opposite signs to those of triangle ABC, you can confirm that Δ A’B’C’ is a 180° rotation of Δ ABC.

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