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The image of the point with coordinates (1,1) under the reflection across the line y=mx+b is the point with coordinates (8,5). Find m+b.

 Nov 27, 2020
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The slope between the given points is   [ 5 - 1 ] / [ 8  -1 ] =  4/7

The slope  of a perpendicular line to the one  through these two points is  -7/4

And  the midpoint between these two points  is  [ ( 8 + 1)/2 , (5 + 1)/2 ]  = ( 9/2, 3 )

 

So....the equation of  a line with a slope of -7/4  through the calculated  midpoint is

 

y = (-7/4) ( x - 9/2) +  3

 

y = (-7/4)x + 63/8 + 3

 

y = (-7/4)x + 87/8  =   the line of reflection

 

m = -7/4       b  =  87/8

 

m + b  =    -7/4 + 87/8   =     -14/8  + 87/8   =    73/8

 

 

cool cool cool

 Nov 27, 2020

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