First slide

Cartesian plane

Question

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

Moderate

A

$(5, 3)$
B

$(- 3, - 5)$
C

$(- 5, - 7)$
D

$(7, 5)$

Solution

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

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