Find the area of the triangle formed by the straight lines whose equations are
$y = m_{1} x + c_{1}$ , $y = m_{2} x + c_{2}$ , and the axis of $y$ .

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Solution

$y = m_{1} x + c_{1} . . . . . . . (i) x = 0 \Rightarrow y = c_{1} A (0, c_{1}) y = m_{2} x + c_{2} . . . . . . . (i) x = 0 \Rightarrow y = c_{2} B (0, c_{2})$

solving $(i)$ and $(i i)$

$Δ = \frac{1}{2} \times b \times h$

$Δ = \frac{1}{2} | A B | | x | Δ = \frac{1}{2} | c_{1} - c_{2} | ∣ ∣ ∣ \frac{c_{2} - c_{1}}{m_{1} - m_{2}} ∣ ∣ ∣ Δ = \frac{1}{2} \frac{{(c_{1} - c_{2})}^{2}}{m_{1} - m_{2}} Δ = \frac{1}{2} {(c_{1} - c_{2})}^{2} \div (m_{1} - m_{2})$

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Similar questions

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

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

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

Find the area of the triangle formed by the lines $y = m_{1} x + c_{1}, y = m_{2} x + c_{2}$ and x = 0

y = m_{1} x + \frac{a}{m_{1}}

y = m_{2} x + \frac{a}{m_{2}}

y = m_{3} x + \frac{a}{m_{3}}

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})

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