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

Solution:

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

The endpoints of the line segment are given as A(3, 4) and B (- 1, 2).

Accordingly, mid-point of AB =( [(3 - 1)/2, (4 + 2)/2]) = (1, 3)

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

Slope of the line perpendicular to AB = - 1/(1/2) = - 2

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

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.3 Question 13

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

Summary:

The equation of the right bisector of the line segment joining the points (3, 4) and (- 1, 2) is 2x + y = 5