Question

Question 13 Find the equation of the right bisector of the line segment joining the points (3, 4) and (–1, 2).

Class X1 - Maths -Straight Lines Page 228

Answer 1

Let
P Ξ (3, 4)
Q Ξ (-1 , 2)

Let B is the midpoint of PQ then,
B Ξ {(x₁ + x₂)/2 , (y₁ + y₂)/2 }
B Ξ {(3 - 1)/2 , (4 + 2)/2 }
B Ξ (1 , 3)

Now, line AB ⊥ line PQ .
slope of AB × slope of PQ = -1
Let slope of line AB is m .
slope of PQ = ( 2 - 4)/(-1 - 3) = -2/-4 = 1/2
m × 1/2 = -1
m = -2

now, equation of line passing through (1, 3) and slope of it -2 is
( y - 3) = -2(x - 1)
y - 3 + 2x - 2 = 0
2x + y - 5 = 0