Question

If $(3,2)$, $(x,\frac{22}{5}),(8,8)$ lie on a line, then $x$ is equal to

• A. $-5$
• B. $2$
• C. $4$
• D. $5$

Answer 1

Answer: (D)

$5$

The area of the triangle made by the points $(x_1,y_1)=(3,2),(x_2,y_2)=(x,\frac{22}{5}),(x_3,y_3)=(8,8)$ will be $=0$, if they lie on the same straight line.

Therefore, the area of the $\Delta =\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

In this case, the area of the triangle

$=\frac{1}{2}[3(\frac{22}{5}-8)+x(8-2)+8(2-\frac{22}{5})]=0$

$\Rightarrow -\frac{54}{5}+6x-\frac{96}{5}=0$

$\Rightarrow 30x=150$

$\Rightarrow x=5$