# A line segment has endpoints at #(1 ,6 )# and #(5 ,2 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?

We have to solve the dilation equation of factor 4 for x and y

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The new endpoints of the line segment after dilation by a factor of 4 around (2, 1) are (5, 17) and (11, -3). The length of the line segment is 10 units.

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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 #(6 ,2 )#, #(5 ,-8 )#, and #(-5 ,3 )#. If the triangle is dilated by a factor of #5 # about point #(7 ,-2 ), how far will its centroid move?
- A line segment has endpoints at #(7 ,2 )# and #(3 ,4 )#. The line segment is dilated by a factor of #6 # around #(4 ,5 )#. What are the new endpoints and length of the line segment?
- Points A and B are at #(9 ,3 )# and #(4 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- A segment with endpoints (5,8) and (-6,8) is rotated around the origin. How long will the new segment be?
- A line segment has endpoints at #(3 ,7 )# and #(4 ,5)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #2 #, and reflected about the y-axis, what will the line segment's new endpoints be?

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