# A line segment has endpoints at #(7 ,6 )# and #(5 ,8 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?

Let the endpoints be A (7 ,6) and B (5 ,8) and their images be A' and B', respectively, under the dilation. Let the centre of dilatation be C (2 ,1)

Similar process to obtain coordinates of B'

The 2 points here are (22 ,21) and (14 ,29)

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The new endpoints of the dilated line segment are (18, 17) and (10, 23). The length of the dilated line segment is 14 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 #(3 ,7 )# and #(5 ,9)#. If the line segment is rotated about the origin by #(pi )/2 #, translated vertically by #2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- Points A and B are at #(3 ,8 )# and #(7 ,3 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #5 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(9 ,3 )# and point B is at #(5 ,-6 )#. Point A is rotated #pi/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?
- Circle A has a radius of #5 # and a center of #(3 ,2 )#. Circle B has a radius of #3 # and a center of #(1 ,4 )#. 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?
- A line segment with endpoints at #(5, 5)# and #(1, 2)# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?

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