# How does dilation affect the length of line segments?

*Dilation* of segment

The length is transformed as

Dilation or scaling is the transformation of the two-dimensional plane or three-dimensional space according to the following rules:

The above properties and other important details about transformation of scaling can be found on Unizor

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Dilation affects the length of line segments by either stretching or compressing them. If the dilation factor is greater than 1, the line segment will be stretched, resulting in a longer length. Conversely, if the dilation factor is between 0 and 1, the line segment will be compressed, leading to a shorter length. However, if the dilation factor is negative, the line segment will be reflected across the line of dilation, but its length will remain the same.

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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.

- Points A and B are at #(3 ,5 )# and #(6 ,1 )#, 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?
- Point A is at #(8 ,7 )# and point B is at #(-3 ,9 )#. 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?
- Points A and B are at #(3 ,7 )# and #(6 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/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?
- Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #6 # and a center of #(7 ,5 )#. If circle B is translated by #<-1 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Circle A has a radius of #1 # and a center at #(2 ,3 )#. Circle B has a radius of #3 # and a center at #(6 ,4 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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