One of the legs of a right triangle measures 9cm and the other leg measures 8cm. Find the measure of the hypotenuse. If necessar
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<h3>Answer:</h3>
(x, y) ⇒ (-y, x)
<h3>Explanation:</h3>A point at y=1 on the y-axis will rotate to the point x = -1 on the x-axis when it is rotated 90° CCW about the origin. Hence the value of x for the image point is the opposite of the y-value of the original point.
A point at x=1 on the x-axis will rotate to the point y=1 on the y-axis when it is rotated 90° CCW about the origin. Hence the value of y for the image point is the x-value of the original point.
In summary, ...
... (x, y) ⇒ (-y, x)
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<em>Comment on rotation matrices</em>
The rotation matrix for rotatation through the angle θ CCW about the origin is ...
When θ = 90°, this matrix becomes ...
and multiplication by coordinates (x, y) gives ...