Question

ABC is a triangle and the coordinates of A, B and C are $(a, b-2c)$, $(a, b+4c)$ and $(-2a,3c)$ respectively where $a$, $b$ and $c$ are positive numbers. The area of the triangle ABC is:

Accepted Answer

D. Base $AB$ lies on line $x = a$. Length of base $AB = |(b+4c) - (b-2c)| = 6c$. Height from $C(-2a, 3c)$ to line $x = a$ is $|a - (-2a)| = 3a$. Area = $\frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes 6c 	imes 3a = 9ac$.

Area of Triangle from Coordinates

Explanation

Practise this under exam conditions