Question

A(6, 3), B(- 3, 5), C(4, - 2) and D(x, 3x) are four points. If $\Delta$DBC: $\Delta$ABC = 1: 2, then x is equal to

• A. $\frac{11}{8}$
• B. $\frac{8}{11}$
• C. 3
• D. None

Answer 1

Answer: (A)

$\Delta DBC=\frac{1}{2}|x\left(5+2\right)3\left(-2+3x\right)+4\left(3x-5\right)|$
$=\frac{1}{2}\left|28x-14\right|=\left|14x-7\right|$
$\Delta ABC=\frac{1}{2}\left|6\left(5+2\right)3\left(2+3\right)4\left(3+5\right)\right|$
$=\frac{49}{2}$
Now $\left|14x-7\right|=\frac{1}{2}\times \frac{49}{2}\Rightarrow x=\frac{11}{8}$ or $-\frac{3}{8}$