Point A is at #(4 ,-2 )# and point B is at #(1 ,-3 )#. 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 point
and No change in distance. Same distance
the equation passing thru the origin (0, 0) and point A(4, -2) is
Use distance formula for "distance from line to a point not on the line"
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The new coordinates of point A after rotating π/2 clockwise about the origin are (-2, -4). The distance between the new point A and point B can be calculated using the distance formula. Then, you can find the difference between the new distance and the original distance between points A and B to determine how much the distance has 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.
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 #(1 ,4 )# and #(5 ,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?
- Points A and B are at #(2 ,9 )# and #(3 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?
- A triangle has corners at #(4 ,-6 )#, #(3 ,-3 )#, and #(8 ,4 )#. If the triangle is dilated by a factor of #1/3 # about point #(-3 ,2 ), how far will its centroid move?
- A triangle has corners at #(3, 4 )#, #( 6, 3 )#, and #( 7 , 2 )#. If the triangle is dilated by # 5 x# around #(1, 1)#, what will the new coordinates of its corners be?
- Circle A has a radius of #4 # and a center of #(8 ,5 )#. 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?

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