# Points A and B are at #(7 ,1 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

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The coordinates of point C after the described transformations are (7, 3).

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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.

- A triangle has corners at #(4, 1 )#, ( 6, -8)#, and #(3, -2 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Point A is at #(-5 ,9 )# and point B is at #(-3 ,4 )#. Point A is rotated #(3pi)/2 # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- Circle A has a radius of #3 # and a center of #(2 ,5 )#. Circle B has a radius of #3 # and a center of #(3 ,8 )#. If circle B is translated by #<4 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Point A is at #(2 ,5 )# and point B is at #(1 ,-6 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?
- A triangle has corners at #(8 ,3 )#, #(4 ,-6 )#, and #(-2 ,5 )#. If the triangle is dilated by a factor of #5 # about point #(1 ,-3 ), how far will its centroid move?

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