+0  
 
+1
110
2
avatar+1442 

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
avatar+87571 
+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

 

 

cool cool cool

CPhill  May 26, 2018
edited by CPhill  May 26, 2018
edited by CPhill  May 26, 2018
 #2
avatar+1442 
+2

Thanks CPhill!

AnonymousConfusedGuy  May 26, 2018

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