# Point A is at #(9 ,3 )# and point B is at #(1 ,-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?

The new coordinates are

The distance has changed by

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The new coordinates of point A after rotating π/2 clockwise about the origin are (-3, 9). The distance between points A and B remains unchanged after the rotation.

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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 ,7 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- A line segment has endpoints at #(1 ,5 )# and #(0 ,1 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 4 #, and reflected about the y-axis, what will the line segment's new endpoints be?
- Point A is at #(6 ,7 )# and point B is at #(-3 ,4 )#. 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?
- Point A is at #(-2 ,5 )# and point B is at #(-3 ,3 )#. 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?
- Points A and B are at #(5 ,9 )# and #(8 ,6 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?

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