Question
D(-4, -9) imagine a 90(counterclockwise) rotation, what would D' be?
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Answered by
GPT-4o mini
To rotate a point counterclockwise by 90 degrees around the origin, you can use the following transformation on the coordinates \((x, y)\):
\[
(x, y) \rightarrow (-y, x)
\]
For the point \(D(-4, -9)\):
- \(x = -4\)
- \(y = -9\)
Applying the transformation:
\[
D' = (-(-9), -4) = (9, -4)
\]
So, after a 90-degree counterclockwise rotation, the new coordinates of point \(D'\) would be \((9, -4)\).
\[
(x, y) \rightarrow (-y, x)
\]
For the point \(D(-4, -9)\):
- \(x = -4\)
- \(y = -9\)
Applying the transformation:
\[
D' = (-(-9), -4) = (9, -4)
\]
So, after a 90-degree counterclockwise rotation, the new coordinates of point \(D'\) would be \((9, -4)\).
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