# A triangle has corners at #(2 ,1 )#, #(4 ,-3 )#, and #(-1 ,4 )#. If the triangle is dilated by a factor of #5 # about point #(4 ,-9 ), how far will its centroid move?

Centroid moves by

Dilated about D(4-9) by a factor of 5

To find new coordinate of centroid G'

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The centroid of a triangle moves proportionally with the scale factor of dilation. Given that the triangle is dilated by a factor of 5 about point (4, -9), the centroid will move 5 times the distance from the center of dilation to the original centroid. Thus, to find how far the centroid moves, we calculate the distance from the center of dilation (4, -9) to the original centroid, then multiply it by 5.

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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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