The equations of the sides of a triangle are $x = 0, y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ . The area of the triangle

\frac{c_{1} - c_{2}}{m_{1} - m_{2}}

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\frac{1}{2} \frac{(c_{1} - c_{2})^{2}}{m_{1} - m_{2}}

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\frac{1}{2} \frac{(c_{1} - c_{2})}{(m_{1} - m_{2})^{2}}

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\frac{(c_{1} - c_{2})^{2}}{(m_{1} - m_{2})^{2}}

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Solution

The correct option is B $\frac{1}{2} \frac{(c_{1} - c_{2})^{2}}{m_{1} - m_{2}}$

Let $x = 0$ is the base of the triangle, and the length of the base of the triangle is $c_{2} - c_{1}$ from the figure.

The height of the triangle is the $x$ coordinate of the point where $y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ meet i.e R.

$m_{1} x + c_{1} = m_{2} x + c_{2} ⟹ x = \frac{c_{2} - c_{1}}{m_{1} - m_{2}}$

Area of the triangle $= \frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times (c_{2} - c_{1}) \times \frac{c_{2} - c_{1}}{m_{1} - m_{2}}$

$∴$ Area $= \frac{1}{2} \frac{(c_{2} - c_{1})^{2}}{| m_{1} - m_{2} |}$

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The equations of the sides of a triangle are x=0,y=m1x+c1 and y=m2x+c2. The area of the triangle

The equations of the sides of a triangle are $x = 0, y = m_{1} x + c_{1}$ and $y = m_{2} x + c_{2}$ . The area of the triangle