What is the image of the point left parenthesis, 6, comma, minus, 1, right parenthesis(6,−1) after a rotation of 270, degrees270 ∘ counterclockwise about the origin?
Question
What is the image of the point left parenthesis, 6, comma, minus, 1, right parenthesis(6,−1) after a rotation of 270, degrees270 ∘ counterclockwise about the origin?
Solution
To find the image of the point (6, -1) after a rotation of 270 degrees counterclockwise about the origin, we can use the rotation matrix for 270 degrees. The rotation matrix for a 270 degree counterclockwise rotation is:
[0 1] [-1 0]
We multiply this matrix by the point (6, -1) to get the new coordinates:
[0 1] * [6] = [06 + 1(-1)] = [-1] [-1 0] [-1] [-16 + 0(-1)] [-6]
So, the image of the point (6, -1) after a rotation of 270 degrees counterclockwise about the origin is (-1, -6).
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