Question

Hey guys! I need a little help and this is a geometry question. What is the image of (8,7) under the reflection of across the line y= -x ?
I would guess (-7, 8).
The CORRECT answer is (-7, -8), but how??

Answer 1

slope of line y=-x is -1
slope of line perpendicular to this line=1
eq of line through (8,7) with slope 1 is
y-7 =1(x-8)
y=x-8+7=x-1
to find point of intersection of y=-x
and y=x-1 is
x-1=-x
x+x=1
x=1/2
y=-x=-1/2
\[point~of~intersection~is \left( \frac{ 1 }{ 2 },\frac{ -1 }{ 2 } \right)\]
let the point of image be (x1,y1)
then
\[\frac{ x1+8 }{ 2 }=\frac{ 1 }{ 2 },x1=1-8=-7\]
\[\frac{ y1+7 }{ 2 }=\frac{ -1 }{ 2 },y1=-1-7=-8\]
point of image is(-7,-8)