# A triangle has corners at #(1 ,3 )#, #(2 ,-2 )#, and #(-8 ,6 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,2 ), how far will its centroid move?

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The centroid of a triangle moves in the same direction and by the same factor as the dilation factor. So, if the triangle is dilated by a factor of 5, the centroid will move 5 times as far from its original position.

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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.

- Circle A has a radius of #4 # and a center of #(8 ,5 )#. Circle B has a radius of #2 # and a center of #(6 ,7 )#. If circle B is translated by #<3 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(-1 ,2 )#, #(3 ,-5 )#, and #(7 ,-3 )#. If the triangle is dilated by a factor of #5 # about point #(-2 ,4 ), how far will its centroid move?
- A line segment has endpoints at #(5 ,1 )# and #(3 ,9 )#. The line segment is dilated by a factor of #5 # around #(2 ,2 )#. What are the new endpoints and length of the line segment?
- A triangle has corners at #(2, -5 )#, ( 6 , 1)#, and #( 4 , 3)#. What will the new coordinates of the triangle be if it is reflected across the x-axis?
- A line segment has endpoints at #(9 ,3 )# and #(5 ,9 )#. The line segment is dilated by a factor of #3 # around #(4 ,4 )#. What are the new endpoints and length of the line segment?

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