Q. 13

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

The right bisector of a line segment bisects the line segment at 90°.

End-points of the line segment AB are given as A (3, 4) and B (–1, 2).

Let mid-point of AB be (x, y)

(x, y) = (7/2, 1/2)

Let slope of line AB be m1

m1 = (2 – 4)/(-1 – 3) = -2/(-4)

m1 = 1/2

Let slope of the line perpendicular to AB be m2

The equation of the line passing through (1, 3) and having a slope of –2 is

(y – 3) = -2 (x – 1)

y – 3 = - 2x + 2

2x + y = 5

Thus, the required equation of the line is 2x + y = 5.

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