Consider the line segment whose endpoints are the x- and y-intercepts of 4 x + y -24 = 0 , and let line l be the perpendicular bisector of this segment. If line l passes through (11, a) , what is the value of a ?
+128408 4x + y - 24 = 0
x intercept = 6 y intercept = 24
So the points are ( 6,0) and ( 0,24)
The midpoint of this segment = ( 3, 12)
And the slope of this segment = -24/6 = -4
So.....the equation of the perpendicular bisector is
y= (1/4) (x - 3) + 12
4y = x - 3 + 48
4y = x + 45
x - 4y + 45 = 0
When x = 11 then
11 - 4a + 45 = 0
56- 4a = 0
56 = 4a
a = 56/4 = 14
See the graph here : https://www.desmos.com/calculator/bi4jwkbp07
