Points A and B are at #(3 ,7 )# and #(2 ,4 )#, respectively. Point A is rotated counterclockwise about the origin by #pi/2 # 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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The coordinates of point C are (5, 5).
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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 triangle has corners at #(7, 2 )#, ( 9, -7)#, and #(1, 4 )#. If the triangle is reflected across the x-axis, what will its new centroid be?
- The line segment XY with endpoints X(3,1) and Y(2,-2) is rotated 90º about the origin. What are the new endpoints of X1 and Y1?
- A line segment has endpoints at #(1 ,4 )# and #(3 ,9 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 2 #, and reflected about the x-axis, what will the line segment's new endpoints be?
- Circle A has a radius of #5 # and a center of #(3 ,2 )#. Circle B has a radius of #2 # and a center of #(1 ,4 )#. If circle B is translated by #<2 ,-1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- How does a vertical translation change the x- and y-coordinates of the endpoints of each side of an angle?

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