The image of the point (-4, 3) under a rotation of 90° (counterclockwise) centered at the origin is ______. Answer in (x, y) format.
Question
The image of the point (-4, 3) under a rotation of 90° (counterclockwise) centered at the origin is ______. Answer in (x, y) format.
Solution 1
To find the image of a point under a rotation of 90° counterclockwise about the origin, we can use the rotation matrix for 90° counterclockwise rotation. The rotation matrix is:
[0 -1] [1 0]
We multiply this matrix by the point (-4, 3) to get the new coordinates.
So,
0*(-4) - 13 = -3 1(-4) + 0*3 = -4
So, the image of the point (-4, 3) under a rotation of 90° counterclockwise centered at the origin is (-3, -4).
Solution 2
To find the image of a point under a rotation of 90° counterclockwise about the origin, we can use the rotation matrix for 90° counterclockwise rotation. The rotation matrix is:
[0 -1] [1 0]
We multiply this matrix by the point (-4, 3) to get the new coordinates.
So,
0*(-4) - 13 = -3 (new x-coordinate) 1(-4) + 0*3 = -4 (new y-coordinate)
So, the image of the point (-4, 3) under a rotation of 90° counterclockwise centered at the origin is (-3, -4).
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