Question

$x + 8y - 22 = 0, 5x + 2y - 34 = 0, 2x - 3y + 13 = 0$ are the three sides of a triangle. The area of the triangle is

• A. 36 square unit
• B. 19 square unit
• C. 42 square unit
• D. 72 square unit

Answer 1

Answer: (B)

If AB denotes : $x +8y -22 = 0 \rightarrow (1)$
BC denotes : $5x +2y-34 = 0 \rightarrow (2)$
and CA denotes : $2x +3y-13 = 0 \rightarrow (3)$
Then solving equations (1), (2) and (3), we get
$A\equiv\left(-2, 3\right), B\equiv\left(6, 2\right)$ and $C\equiv\left(4, 7\right).$
Hence, area of $\Delta ABc$ is 19 square units