Question

What is the value of y if $(y,3),(-5,6)$ and $(-8,8)$ are collinear?

• A. $-1$
• B. $2$
• C. $\frac{1}{2}$
• D. $-\frac{1}{2}$

Answer 1

The correct option is D $-\frac{1}{2}$

Let $A(y,3),B(-5,6)$ and $C(-8,8)$ be the given points.

where $x_1=y,y_1=3$, $x_2=-5,y_2=6$, $x_3=-8,y_3=8$

Condition for collinear equation:

Area of triangle $=0$

$\frac{1}{2}|\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]|=0$

$\Rightarrow y(6-8)+(-5)(8-3)+(-8)(3-6)=0$

$\Rightarrow 6y-8y-40+15-24+48=0$

$\Rightarrow -2y-1=0$

$\Rightarrow -2y=1$

$\Rightarrow y=-\frac{1}{2}$