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General Form of a Straight Line

The area of ...

Question

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

(5, 3)

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(- 3, - 5)

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(- 5, - 7)

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(7, 5)

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Solution

The correct options are
B $(7, 5)$
D $(- 3, - 5)$
Let any point on the line $x - y = 2$ be $C \equiv (h, h - 2)$ . Given area of $Δ A B C$ is
$∣ ∣ ∣ ∣ \frac{1}{2} ∣ ∣ ∣ ∣ \begin{matrix} h & h - 2 & 1 - 5 & 0 & 1 3 & 0 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ = 20$
$\Rightarrow | 8 (h - 2) | = 40$
$\Rightarrow h - 2 = \pm 5$
$\Rightarrow h = 7, - 3$
Hence, the points are $(7, 5)$ and $(- 3, - 5)$ .

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The area of △ABC is 20 cm2. The coordinates of vertex A are (−5,0) and those of B are (3,0). The vertex C lies on the line x−y=2. The coordinates of C can be

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