Question

The line segment between (9,6) and (-2,-1) is bisected at (3.5,2.5). Find the y-intercept of the perpendicular bisector.

Ans: y-intercept = (0, _____)

Answer 1

Y-intercept is (0,8)

Explanation:

Firstly, we need to get the equation of the line segment

We have the general equation as;

y = mx + b

m is the slope and b is the y-intercept

So for the slope between (9,6) and (-2,-1); we have

m = (y2-y1)/(x2-x1)

m = (-1-6)/(-2-9) = -7/-11 = 7/11

Mathematically, when two lines are perpendicular, their slopes have a product of -1

Let the slope of the second line be m

m * 7/11 = -1

7m = -11

m = -11/7

The equation of the second line is;

y = mx + b

y = -11x/7 + b

The line passes through the point (3.5,2.5)

So,

2.5 = -11/7(3.5) + b

2.5 = -5.5 + b

b = 2.5 + 5.5

b = 8

so the y-intercept of the perpendicular bisector is 8