# Points A and B are at #(8 ,3 )# and #(1 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #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 rotating point A counterclockwise by π/2 about the origin and dilating it by a factor of 2 about point C are (-3, 1).

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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.

- CD has endpoints, C( -8, 3) and D (-8, -6) Rotate the segment about the origin, 90 clockwise. What are the coordinates of C' and D'?
- Circle A has a radius of #2 # and a center at #(3 ,1 )#. Circle B has a radius of #4 # and a center at #(8 ,3 )#. If circle B is translated by #<-4 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Point A is at #(8 ,-1 )# and point B is at #(9 ,-7 )#. 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?
- A line segment has endpoints at #(4 ,5 )# and #(2 ,3 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- A triangle as corners at #(5 ,2 )#, #(2 ,4 )#, and #(3 ,8 )#. If the triangle is dilated by a factor of #3 # about #(2 ,3 ), how far will its centroid move?

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