Find the value of `a`for which …
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Sia ? 6 years, 5 months ago
Let A(a, 2a), B(-2, 6) and C(3, 1) be the given points.
{tex}\Delta{/tex}Area of {tex}\Delta{/tex}ABC
{tex} = \frac{1}{2}\left\{ {a\left( {6 - 1} \right) + \left( { - 2} \right)\left( {1 - 2a} \right) + 3\left( {2a - 6} \right)} \right\}{/tex}
{tex} = \frac{1}{2}\left\{ {5a - 2 + 4a + 6a - 18} \right\}{/tex}
{tex} = \frac{1}{2}\left\{ {15a - 20} \right\}{/tex}
Since, Area of {tex}\Delta{/tex}ABC = 10 (given)
{tex} \Rightarrow \frac{1}{2}\left\{ {15a - 20} \right\} = 10{/tex}
{tex}\Rightarrow{/tex} 15a - 20 = 20
{tex}\Rightarrow{/tex} 15a = 40
{tex} \Rightarrow a = \frac{{40}}{{15}}{/tex}
{tex} \Rightarrow a = \frac{8}{3}{/tex}
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