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