A line segment has endpoints at #(1 ,2 )# and #(3 ,4 )#. 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?

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Answer 1 · 2016-10-03T17:35:43

(-2,-4) and (-4,-6)

First graph the two points. (I am unable to graph a line segment so this is a line through the two points.)

graph{x+1 [-10, 10, -5, 5]}

Then you can either rotate the line segment to the right three times or to the left once. (remember it is about the origin)

graph{-x-1 [-10, 10, -5, 5]}

Then add three to the y-values of the current points.

graph{-x+2 [-14.24, 14.24, -7.12, 7.12]}

Finally flip it over the x-axis.

graph{x-2 [-14.24, 14.24, -7.12, 7.12]}