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

New endpoints

New Length

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The new endpoints of the dilated line segment are (1.5, 3.25) and (2.5, 3.75). The length of the line segment after dilation is 0.707 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 line segment has endpoints at #(5 ,8 )# and #(7 ,4)#. If the line segment is rotated about the origin by #pi #, translated horizontally by #-1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- Point A is at #(-7 ,-1 )# and point B is at #(2 ,-4 )#. 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?
- Circle A has a radius of #5 # and a center of #(2 ,7 )#. Circle B has a radius of #1 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(1 ,5 )# and #(2 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?
- A line segment has endpoints at #(5 ,9 )# and #(8 ,2 )#. The line segment is dilated by a factor of #2 # around #(5 ,3 )#. What are the new endpoints and length of the line segment?

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