The graph of the line x + y = b is a perpendicular bisector of the line segment from (1,3) to (7,9). What is the value of b?
+128473 The slope of this segment is [ 9 - 3 ] / [ 7 - 1 ] = 6/6 = 1
The perpendicular line to this segment will have a negative reciprocal slope = -1
Since this line is a perpendicular bisector, we need to find the mdpoint of the segment.....this is given by
( [ 1+ 7] / 2 , [ 3 + 9] / 2 ) = (8/2 , 12/2 ) = (4, 6)
The equation of the perpendicular line is
y = -1 ( x -4) + 6
y = -x + 4 + 6 add x to both sides and simplify
x + y = 10
So...b = 10
