# A line segment has endpoints at #(1 ,6 )# and #(6 ,7 )#. The line segment is dilated by a factor of #4 # around #(4 ,3 )#. What are the new endpoints and length of the line segment?

I did the general case here.

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The new endpoints of the line segment after dilation by a factor of 4 around the point (4, 3) are:

Endpoint 1: (13, 18) Endpoint 2: (19, 19)

The length of the line segment after dilation 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.

- Circle A has a radius of #2 # and a center of #(6 ,5 )#. Circle B has a radius of #3 # and a center of #(2 ,4 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(8 ,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 #3 #. If point A is now at point B, what are the coordinates of point C?
- A line segment has endpoints at #(5 ,8 )# and #(2 , 1)#. The line segment is dilated by a factor of #1/2 # around #(3 , 5)#. What are the new endpoints and length of the line segment?
- A triangle has corners at #(4, 4 )#, ( 3, -2)#, and #( 5, -3)#. If the triangle is reflected across the x-axis, what will its new centroid be?
- Point A is at #(-4 ,5 )# and point B is at #(-3 ,7 )#. 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?

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