Question

Plot the triangle whose vertices areA(-2,-4) B(5,-4) and C(5,6).Find the area of the triangle in square units (3marks).

Answer 1

$\textbf{\underline{\pink{\underline{\large{Step by step Explanation:-}}}}}$

$\textit{\underline{Given,,}}$

$\mathtt{x_{1}=-2,,y_{1}=-4,,x_{2}=5,,y_{2}=-4,,x_{3}=5,,y_{3}=6}$

$\textit{\underline{We know that,,ar(<strong>ABC</strong><strong>)</strong><strong>=</strong>}}$

$\mathrm{\boxed{\pink{\frac{1}{2}[x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})]}}}$

$\textit{\underline{Hence,,}}$

$\mathrm{ar(\triangle{ABC})=\frac{1}{2}[-2(5-6)+5(6-(-4))+5(-4-(-4))]}$

$\mathrm{=\frac{1}{2}[-2(-1)+5(6+4)+5(-4+4)]}$

$\mathrm{=\frac{1}{2}[2+5(10)+5(0)]}$

$\mathrm{=\frac{1}{2}[2+50+0]}$

$\mathrm{=\frac{1}{2}[52]}$

$\mathrm{=26,, unit^{2}}$

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