Points A and B are at #(5 ,8 )# and #(3 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
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To find the coordinates of point C, we first need to perform the rotation and dilation operations on point A to get to point B.
Rotation by π/2 counterclockwise about the origin changes the coordinates (x, y) to (-y, x).
So, for point A (5, 8), after rotation, it becomes (-8, 5).
Then, dilation about point C by a factor of 3 means multiplying the coordinates by 3. So, the new coordinates become (-8 * 3, 5 * 3) = (-24, 15).
Since point A after rotation and dilation is now at point B (3, 2), point C is the center of dilation. Therefore, the coordinates of point C are (-24, 15).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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