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

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3 years ago