# A line segment has endpoints at #(4 ,7 )# and #(5 ,6)#. If the line segment is rotated about the origin by #pi #, translated vertically by #-2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

#color(chocolate)("After all 3 transformations " color(gray)((4, 7)to(-4, 9)" and "(5, 6)to(-5, 8)#

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The line segment's new endpoints after the described transformations will be (-7, -4) and (-6, -5).

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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 #(7 ,4 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #(3 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 #(8 ,3 )# and #(1 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- A line segment has endpoints at #(2 , 3)# and #(1 , 2)#. If the line segment is rotated about the origin by #(pi)/2 #, translated vertically by #4#, and reflected about the x-axis, what will the line segment's new endpoints be?
- A triangle has corners at #(2 ,1 )#, #(4 ,-3 )#, and #(-1 ,4 )#. If the triangle is dilated by a factor of #5 # about point #(4 ,-9 ), how far will its centroid move?
- How does dilation affect the length of line segments?

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