First slide

Cartesian plane

Question

$A (- 5, 0)$ and $B (3, 0)$ are two of the vertices of a triangle $A B C .$ Its area is 20 square ems. The vertex $C$ lies on the line $x - y = 2 .$ The coordinates of $C,$ are

Moderate

A

$(- 7, - 5)$ or $(3, 5)$
B

$(- 3, - 5)$ or $(- 5, 7)$
C

$(7, 5)$ or $(3, 5)$
D

$(- 3, - 5)$ or $(7, 5)$

Solution

Let the coordinates of the third vertex C be $(h, k) .$
Then, Area of $A B C = 20 s q .$ units
$\Rightarrow \frac{1}{2} |\begin{array}{rrr} h k 1 \\ - 5 0 1 \\ 3 0 1 \end{array}| = \pm 20 \Rightarrow k = \pm 5$ . …(i)
Since, $(h, k)$ lies on $x - y = 2$ Therefore,
$h - k = 2$ …(ii)
Solving (i) and (ii), we find that the coordinates of the third vertex are $(- 3, - 5) o r, (7, 5) .$

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