Question

If three lines whose equations are y=m₁ x+c₁, y=m₂ x+c₂ and y=m₃ x+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

 

is the point of intersection of lines (1) and (2).

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).