Question
On a coordinate plane, a triangle has points A (negative 5, 3), B (negative 2, 4), C (negative 2, 2).
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
Triangle ABC is shown on the graph. What are the coordinates of the image of point B after the triangle is rotated 270° about the origin?
(4, 2)
(2, 4)
(–4, –2)
(–2, –4)
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To rotate a point \((x, y)\) about the origin by 270° (which is equivalent to a 90° clockwise rotation), you can use the following transformation:
\[
(x, y) \rightarrow (y, -x)
\]
We need to apply this transformation to point B which has coordinates \((-2, 4)\).
Applying the transformation:
\[
(-2, 4) \rightarrow (4, -(-2)) = (4, 2)
\]
Therefore, the coordinates of the image of point B after the triangle is rotated 270° about the origin are \((4, 2)\).
The correct answer is:
\((4, 2)\)
\[
(x, y) \rightarrow (y, -x)
\]
We need to apply this transformation to point B which has coordinates \((-2, 4)\).
Applying the transformation:
\[
(-2, 4) \rightarrow (4, -(-2)) = (4, 2)
\]
Therefore, the coordinates of the image of point B after the triangle is rotated 270° about the origin are \((4, 2)\).
The correct answer is:
\((4, 2)\)
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