# A line segment has endpoints at #(1 ,4 )# and #(3 ,4 )#. The line segment is dilated by a factor of #6 # around #(2 ,5 )#. What are the new endpoints and length of the line segment?

New endpoints:

New line segment length:

Note that the distance between the initial line segment end points:

Dilating by a factor of

Consider the vectors from the point of dilation:

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The new endpoints of the line segment after dilation are (7, 4) and (11, 4). The length of the line segment remains the same after dilation, which is 2 units.

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- Circle A has a radius of #2 # and a center of #(5 ,7 )#. Circle B has a radius of #4 # and a center of #(3 ,8 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(4 ,3 )# and #(5 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/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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- A line segment with endpoints at #(1 , -2 )# and #(1, 8 )# is rotated clockwise by #(3 pi)/2#. What are the new endpoints of the line segment?
- Points A and B are at #(4 ,1 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

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