Question

If three lines whose equations are y = m₁x + C₁,y = m₂x + C₂ and y = m₃x +C₃ are 

concurrent, then show that m₁ (C₂ - C₃) + m₂ (C₃ - C₁) + m₃ (C₁ - C₂)=0.

Answer 1

The equations of the given lines are
y = m1x + c1 ……………………. (1)
y = m2x + c2 ………………….… (2)
y = m3x + c3 ……………………. (3)
On subtracting equation (1) from (2), we obtain

On substituting this value of x in (1), we obtain

It is given that lines (1), (2), and (3) are concurrent. Hence, the point of intersection of lines (1) and (2) will also satisfy equation (3).