Question

Find the equation of the straight line which bisects the distance the points A(a, b) and B(a’, b’) and also bisects the distance between the points A(a, b) and B(a’, b) and also bisects the distance between the points C(– a, b) and D(a’, – b’)

Answer 1

Co-ordinate of mid-point of A(a, b), B(a’, b’) are

\((\frac{a+a'}{2},\frac{b+b'}{2})\), and co-ordinate of mid-point of 

C(– a, b), D(a’, – b’) are \((\frac{-a+a'}{2},\frac{b-b'}{2})\). Now, the equation of the line passing through (x₁, y₁) and (x₂, y₂) is

y − y₁ = \(\frac{y_2-y_1}{x_2-x_1}\) (x− x₁)

Here,

   

⇒ 2b’ x – 2ay + (ab – a’ b’ + ab’) = 0, is the required equation of the line.