Question

A line segment has endpoints at (–1, 4) and (4, 1). Which reflection will produce an image with endpoints at (–4, 1) and (–1, –4)?

Answer 1

let be (x, y)=(-1, 4) according to question its image is (x', y')=(- 4,1).and as we see x'= -4=-y, and y'=1=-(-1)=-x, besides when (x, y)=(4, 1) its image is (x', y')=(-1, -4), as the same of the previous remark, x'=-1= -y,and y'=-4=- (4)=-x, generally x=-y, therefore the line segment which is a reflection is y= -x.Hope this helps. Let me know if you need additional help!