A line segment has endpoints at #(4 ,5 )# and #(2 ,3 )#. If the line segment is rotated about the origin by #( 3 pi)/2 #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Answer 1

The new end points are #(-2, -2)# and #(-4, -4)#

Considering the end point #(2, 3)# rotated #+(3pi)/2# about the origin #(0, 0)#, it will end up exactly at #(3, -2)#. Translating that -1 horizontally will place it at #(2, -2)# then reflecting about the y-axis will place it at #(-2,-2)# at the 3rd Quadrant.

Considering the end point #(4, 5)# rotated #+(3pi)/2# about the origin #(0, 0)#, it will end up exactly at #(5, -4)#. Translating that -1 horizontally will place it at #(4, -4)# then reflecting about the y-axis will place it at #(-4,-4)# at the 3rd Quadrant also.

Therefore the new end points are

#(-2, -2)# and #(-4, -4)#

have a nice day! from the Philippines !

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Answer 2

Ella Armstrong

The new endpoints of the line segment after the described transformations will be: Endpoint 1: (-5, 4) Endpoint 2: (-3, 2)

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Answer from HIX Tutor

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.