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

Dilation is a fancy word for scale. As soon as you talk about scale your are dealing with ratios. Dilation that is positive increases the magnitude. Assuming positive dilation as not indicated otherwise.

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Length

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The new endpoints of the line segment after dilation by a factor of 3 around (6, 2) are (15, 16) and (12, 7). The length of the line segment remains the same after dilation, so the length is still √((12 - 15)^2 + (7 - 16)^2) = √((-3)^2 + (-9)^2) = √(9 + 81) = √90 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.

- Identify the reflection rule on a coordinate plane that verifies that triangle A(-1,7), B(6,5), C(-2,2) and A'(-1,-7), B'(6,-5), C'(-2,-2) triangle are congruent when reflected over the x-axis?
- Point A is at #(8 ,-2 )# and point B is at #(5 ,-7 )#. 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?
- A triangle has corners at #(-3 ,5 )#, #(7 ,6 )#, and #(1 ,-4 )#. If the triangle is dilated by a factor of #2/3 # about point #(-3 ,4 ), how far will its centroid move?
- Points A and B are at #(5 ,9 )# and #(3 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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?
- Circle A has a radius of #4 # and a center of #(6 ,2 )#. Circle B has a radius of #2 # and a center of #(5 ,7 )#. If circle B is translated by #<-2 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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