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.
+128473 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
