If three lines whose equations are

concurrent, then show that

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Solution

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).

Hence,

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Similar questions

y = m_{1} x + c_{1}, y = m_{2} + c_{2} a n d y = m_{3} x + c_{3}

m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0

y = m_{1} x + c_{1}, y = m_{2} x + c_{2}

y = m_{2} x + c_{2}

m_{1} (c_{2} - c_{1}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0

y = m_{1} x + c_{1}, y = m_{2} x + c_{2}

y = m_{3} x + c_{3}

m_{1} (c_{2} - c_{1}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2})

If the three lines $y = m_{1} x + c_{1}, y = m_{2} x + c_{2}$ and $y = m_{3} x + c_{3}$ are concurrent then show that,

$m_{1} (c_{2} - c_{3}) + m_{2} (c_{3} - c_{1}) + m_{3} (c_{1} - c_{2}) = 0$

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