# A line segment has endpoints at #(3 ,4 )# and #(2 ,5 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

The new end points are

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The new endpoints of the line segment after rotation, horizontal translation, and reflection about the x-axis are (-5, 2) and (-4, 3).

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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.

- Circle A has a radius of #3 # and a center of #(2 ,1 )#. Circle B has a radius of #4 # and a center of #(7 ,3 )#. If circle B is translated by #<-3 ,2 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A triangle has corners at #(3, 8 )#, #( 2, 1 )#, and #( 9 , 6 )#. If the triangle is dilated by # 3 x# around #(1, 2)#, what will the new coordinates of its corners be?
- A line segment has endpoints at #(1 ,4 )# and #(7 ,3 )#. The line segment is dilated by a factor of #3 # around #(2 ,6 )#. What are the new endpoints and length of the line segment?
- A line segment with endpoints at #(1 , -2 )# and #(1, -4 )# is rotated clockwise by #pi/2#. What are the new endpoints of the line segment?
- Point A is at #(-3 ,-4 )# and point B is at #(5 ,8 )#. Point A is rotated #pi # 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?

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