The area of triangle $ABC$ is $20{ ext{ }cm}^{2}$. The coordinates of vertex $A$ are $( - 5,0)$ and

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The area of triangle $ABC$ is $20{	ext{ }cm}^{2}$. The coordinates of vertex $A$ are $( - 5,0)$ and $B$ are $(3,0)$. The vertex $C$ lies on the line $x - y = 2$. The coordinates of $C$ are:

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Sol. [Key Concept: $C$ on $x - y = 2$ with $\frac{1}{2} \cdot \ AB \cdot \ h = 20$ gives two positions.]Let $C \equiv (\lambda,\lambda - 2)$$$\begin{matrix} \frac{1}{2} 	imes 8 & \ 	imes |\lambda - 2| = 20 \ \Rightarrow \lambda - 2 & \ = \pm 5,\ \lambda = 7, - 3 \ C & \ \equiv (7,5),( - 3, - 5) \end{matrix}$$✘ (a) $(5,3)$ does not give area 20.✔ (b) $(7,5)$ lies on $x - y = 2$ and gives area 20.✘ (c) $( - 5, - 7)$ does not give area 20.✔ (d) $( - 3, - 5)$ lies on $x - y = 2$ and gives area 20.

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