# A line segment has endpoints at #(0 ,2 )# and #(3 ,5 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated vertically by # 3 #, and reflected about the x-axis, what will the line segment's new endpoints be?

Since there are 3 transformations to be performed here, name the endpoints A (0 ,2) and B (3 ,5) so that they may be 'tracked' after each transformation.

a point (x ,y) → (y ,-x)

hence A(0 ,2) → A'(2 ,0) and B(3 ,5) → B'(5 ,-3)

a point (x ,y) → (x ,y+3)

hence A'(2 ,0) → A''(2 ,3) and B'(5 ,-3) → B''(5 ,0)

Third transformation Under a reflection in the x-axis

a point (x ,y) → (x ,-y)

hence A''(2 ,3) → A'''(2 ,-3) and B''(5 ,0) → B'''(5 ,0)

Thus after all 3 transformations:

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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.

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- Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #4 # and a center of #(7 ,5 )#. If circle B is translated by #<-1 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

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