A line segment has endpoints at #(8 ,5 )# and #(2 ,3 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?
Sadie AdamsThe new endpoints are
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Savannah AguilarThe new endpoints of the line segment after the described transformations are: (-5, -3) and (-9, -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.
- Points A and B are at #(1 ,8 )# and #(3 ,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?
- A triangle has corners at #(1 ,5 )#, #(-1 ,-4 )#, and #(5 ,-6 )#. If the triangle is dilated by a factor of #2 # about point #(-2 ,-3 )#, how far will its centroid move?
- Circle A has a radius of #6 # and a center of #(4 ,3 )#. Circle B has a radius of #3 # and a center of #(1 ,8 )#. If circle B is translated by #<-2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Circle A has a radius of #5 # and a center of #(6 ,1 )#. Circle B has a radius of #1 # and a center of #(4 ,5 )#. If circle B is translated by #<-3 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
- Points A and B are at #(6 ,3 )# and #(1 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #pi # 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?
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