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

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The centroid of a triangle moves by the same factor as the dilation. Since the triangle is dilated by a factor of 2, the centroid will move twice the distance from its original position to the center of dilation. Therefore, the distance the centroid will move is (2 \times \text{distance from centroid to center of dilation}). Calculate the distance between the centroid of the original triangle and the center of dilation using the distance formula. Then, multiply this distance by 2 to find how far the centroid will move.

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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 #(3, 1 )#, #( 2, 3 )#, and #( 5 , 6 )#. If the triangle is dilated by # 2/5 x# around #(1, 2)#, what will the new coordinates of its corners be?
- A triangle has corners at #(8, 3 )#, ( 5, -8)#, and #(7, -4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- A triangle has corners at #(7 ,3 )#, #(9 ,4 )#, and #(5 ,2 )#. If the triangle is dilated by a factor of #2 # about point #(6 ,1 ), how far will its centroid move?
- A line segment has endpoints at #(7 , 4)# and #(2 , 5)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-3#, and reflected about the y-axis, what will the line segment's new endpoints be?
- Point A is at #(-8 ,2 )# and point B is at #(2 ,-1 )#. Point A is rotated #pi/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?

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