Question

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

Answer 1

Step-by-step explanation:

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

∘

.

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

Accordingly, mid-point of AB ={

2

3−1

,

2

4+2

}=(1,3)

and slope of AB =

−1−3

2−4

=

−4

−2

=

2

1

∴ slope of line perpendicular to AB =−

{

2

1

}

1

=−2

Thus equation of the line passing through (1,3) and having a slope of −2 is given by,

(y−3)=−2(x−1)

⇒y−3=−2x+2⇒2x+y=5

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