Asked by Story
On a coordinate plane, 2 squares are shown. The first square has points A (1, 1), B (4, 1), C (4, 4), D (1, 4). The second square has points A prime (negative 1, negative 4), B prime (negative 4, negative 4), C prime (negative 4, negative 1), D prime (negative 1, negative 1).
Micaela tried to rotate the square 180° about the origin. Is her rotation correct? If not, explain why.
No, she translated the figure instead of rotating it.
No, she reflected the figure instead of rotating it.
No, the vertices of the image and pre-image do not correspond.
Yes, the rotation is correct.
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Answered by
GPT-5 mini
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No — the vertices do not correspond.
A 180° rotation about the origin sends (x,y) to (−x,−y). So
A(1,1) → (−1,−1),
B(4,1) → (−4,−1),
C(4,4) → (−4,−4),
D(1,4) → (−1,−4).
Those four points are exactly the points of A′B′C′D′, but the labels are mismatched: A rotated to (−1,−1) (which is D′), B → C′, C → B′, D → A′. Thus the image is the correct rotated square but the vertex labels do not correspond.
A 180° rotation about the origin sends (x,y) to (−x,−y). So
A(1,1) → (−1,−1),
B(4,1) → (−4,−1),
C(4,4) → (−4,−4),
D(1,4) → (−1,−4).
Those four points are exactly the points of A′B′C′D′, but the labels are mismatched: A rotated to (−1,−1) (which is D′), B → C′, C → B′, D → A′. Thus the image is the correct rotated square but the vertex labels do not correspond.
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