Points (1, 7) and (-3, 2)
Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)
The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4
Slope = 5/4
Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5
By condition of perpendicularity
For points (1, 7) and (-3, 2),
Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)
Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)
= (-1, 9/2)
Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)
Equation y - y₁ = m (x - x₁)
y - 9/2 = (-4/5) (x - -1)
y - 9/2 = (-4/5)(x + 1)
5(y - 9/2) = -4(x + 1)
5y - 45/2 = -4x - 4
5y = -4x - 4 + 45/2
5y + 4x = 45/2 - 4
5y + 4x = 22 1/2 - 4 = 18 1/2
5y + 4x = 37/2
10y + 8x = 37
The equation of the line to perpendicular bisector is 10y + 8x = 37
