#### Question

If three lines whose equations are y = m_{1}x + c_{1}, y = m_{2}x + c_{2} and y = m_{3}x + c_{3} are concurrent, then show that m_{1}(c_{2} – c_{3}) + m_{2} (c_{3} – c1) + m_{3} (c_{1} – c_{2}) = 0.

#### Solution

The equations of the given lines are

*y* = *m*_{1}*x* + *c*_{1} … (1)

*y* = *m*_{2}*x* + *c*_{2} … (2)

*y* = *m*_{3}*x* + *c*_{3} … (3)

On subtracting equation (1) from (2), we obtain

Is there an error in this question or solution?

Solution 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. Concept: General Equation of a Line.