We are given two points which are
(-9, -1) and (3, -7)
Firstly, find the mid point of the two points
Midpoints = x1 + x2 / 2 , y1 + y2 / 2
From the point given
x1 = -9, y1 = -1, x2 = 3 and y2 = -7
Mid-point
x1 + x2 / 2
-9 + 3 / 2
= -6/2
= -3
y1 + y2 / 2
-1 + (-7) / 2
= -1 - 7 / 2
= - 8/2
= -4
The midpoint of the points (-9, -1) and (3, -7) is (-3, -4)
Mid-point = (-3, -4)
Secondly, find the slope
Slope = Rise / Run
Rise = y2 - y1
Run = x2 - x1
Rise = -7 -(-1)
Rise = -7 + 1
Rise = -6
Run = 3 - (-9)
Run = 3 + 9
Run = 12
Slope = Rise / Run
Slope = -6/12
Slope = -1/2
Since it bisect perpendicularly
Hence, m1 x m2 = -1
Where m1 = -1/2
-1/2 x m2 = -1
-m2/2 = -1
Cross-multiply
-m2 = 2 x -1
-m2 = -2
Divide both sides by -1
-m2 /-1 = -2/-1
m2 = 2
The equation of a straight line is
y - y1 = m(x - x1)
y1 = -1 and x1 = -9
y - (-1) = 2(x - (-9)]
y + 1 = 2(x + 9)
y + 1 = 2*x + 2*9
y + 1 = 2x + 18
Make y the subject of the formula
y = 2x + 18 - 1
y = 2x + 18 - 1
y = 2x + 17
The equation is y = 2x + 17
-9
