Question

If the area of the triangle formed by $(-2,5),(x,-3)$ and $(3,2)$ is $14$ square units, then $x=$ ____.

• A. 1
• B. 2
• C. -2
• D. -1

Answer 1

Answer: (B)

Area of triangle having vertices $(x_1,y_1),(x_2,y_2)$ and $(x_3,y_3)$ is given by
$=\frac{1}{2}\times \left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$\therefore Area=\frac{1}{2}[-2(-3-2)+x(2-5)+3(5+3)]$
$=\frac{1}{2}[10-3x+24]=\frac{34-3x}{2}$
$\therefore \frac{34-3x}{2}=14$ or x = 2