+93 The graph of the line x+y=b is a perpendicular bisector of the line segment from (1,3) to (5,7). What is the value of b?
+23246 1) Find the midpoint of the line segment: mdpt = ( (1 + 5)/2, (3 + 7)/2 ) = ( 3, 5 )
2) Find the slope of the line segment: m = (y2 - y1) / (x2 - x1) = (7 - 3) / (5 - 1) = 4/4 = 1
3) The slope of the perpendicular bisector will be the negative reciprocal of the slope found in 2).
m = -1
4) We have a point (3, 5) and a slope -1, so we can use the point-slope form:
y - y1 = m(x - x1) ---> y - 5 = -1(x - 3)
5) Rewrite this equation: y - 5 = -1(x - 3)
y - 5 = -x + 3
y = -x + 8
x + y = 8
