The image of the point with coordinates (1,1) under the reflection across the line y=mx+b is the point with coordinates (9,5). Find m+b.

Thanks!

AnonymousConfusedGuy
May 26, 2018

#1**+1 **

The midpoint of the line connecting these two points will lie on the line we seek...and this is

[ (1 + 9 ) / 2, ( 1 + 5) / 2 ] = [ 5, 3 ]

And the slope of this line connecting the given points is [ 5 - 1 ] / [ [ 9 - 1] = 4/8 = 1/2

And the line we seek is perpendicular to this line...so its slope is - 2

And the equation of this line is

y = -2 (x - 5) + 3

y = - 2x + 10 + 3

y = - 2x + 13

So...m + b = -2 + 13 = 11

Here's a pic : https://www.desmos.com/calculator/jdelhysrdy

CPhill
May 26, 2018