# Point A is at #(4 ,-5 )# and point B is at #(-6 ,-2 )#. 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?

New coordinates

Change in distance

Coordinates of A’ (-5,-4)

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The new coordinates of point A after rotating (3π)/2 clockwise about the origin are (5, 4). The distance between points A and B remains unchanged after the rotation. Therefore, the distance between points A and B has not changed.

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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.

- Identify the rotation rule on a coordinate plane that verifies that triangle A(2,-1), B(4,1), C(3,3) and triangle A'(-2, 1), B'(-4,-1), C'(-3,-3) are congruent when rotated 180°?
- A triangle has corners at #(3, 1 )#, #( 2, 3 )#, and #( 2 , 6 )#. If the triangle is dilated by # 1/5 x# around #(1, 1)#, what will the new coordinates of its corners be?
- Point A is at #(-6 ,1 )# and point B is at #(3 ,8 )#. 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?
- A line segment goes from #(1 ,1 )# to #(4 ,2 )#. The line segment is reflected across #x=2#, reflected across #y=-1#, and then dilated about #(1 ,1 )# by a factor of #2#. How far are the new endpoints from the origin?
- What are the coordinates of the image of point #A(2,-7)# under the translation #(x,y)-> (x-3,y+5)#?

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