# A line segment has endpoints at #(4 ,0 )# and #(2 ,9 )#. If the line segment is rotated about the origin by #( pi)/2 #, translated vertically by #-8 #, and reflected about the x-axis, what will the line segment's new endpoints be?

The endpoints are

The rotated angle

The rotated angle

Reflect about the x axis:

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The new endpoints of the line segment after rotation by ( \frac{\pi}{2} ), vertical translation by -8, and reflection about the x-axis are (8, -6) and (-9, -2).

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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 , 4)# and #(1 ,9)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the x-axis, what will the line segment's new endpoints be?
- A line segment has endpoints at #(3 ,8 )# and #(5 , 9)#. The line segment is dilated by a factor of #3 # around #(2 , 3)#. What are the new endpoints and length of the line segment?
- A triangle has corners at #(1 ,5 )#, #(3 ,-9 )#, and #(-1 ,-4 )#. If the triangle is dilated by a factor of #5 # about point #(-1 ,-2 ), how far will its centroid move?
- What are the coordinates of point A (4,-1) after it has been reflected over the y-axis?
- Points A and B are at #(2 ,4 )# and #(7 ,5 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/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?

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