# 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?

Oct 3, 2016

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

#### Explanation:

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]}