Question

Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).

Answer 1

Let the midpoint of the line segment joining the points A(3, 4) and B(−1, 2) be

`"D"((3 - 1)/2, (4 + 2)/2)` or D(1, 3)

Slope of AB, m₁ = `(2 - 4)/(-1 -3) = (-2)/(-4) = 1/2`

Let the second line CD be perpendicular to the line AB.

∴ Slope of CD = `- 1/"m"_1 = -1/(1/2) = -2`

Line CD passes through point D

∴ Equation of line CD

y – 3 = –2(x – 1)

= –2x + 2

∴ 2x + y – 5 = 0

Hence, the required equation is 2x + y = 5.