A line segment goes from #(3 ,2 )# to #(1 ,3 )#. The line segment is dilated about #(1 ,1 )# by a factor of #2#. Then the line segment is reflected across the lines #x=1# and #y=-3#, in that order. How far are the new endpoints from the origin?
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The new endpoints of the line segment after dilation and reflection are approximately (4.5, -5.5) and (0.5, -0.5). The distance of these endpoints from the origin can be calculated using the distance formula, resulting in approximately 7.778 units.
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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.
- Points A and B are at #(2 ,4 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- If rectangle DEFG is dilated by a scale factor of 1/2 with a dilation center of (0, 0), what will be the coordinates of point F'?
- Points A and B are at #(9 ,9 )# and #(7 ,8 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # and dilated about point C by a factor of #2 #. If point A is now at point B, what are the coordinates of point C?
- Points A and B are at #(4 ,9 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?
- Point A is at #(6 ,4 )# and point B is at #(-2 ,7 )#. 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?

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