Question

Choose the possible value of a such that point (3a, a) will be collinear with points (6,2) and (-4,-1).

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

To check whether the given points are collinear or not, we check the slopes.
The slope of any two points taken at a time out of the three points will always be the same.

Slope = $\frac{y_2-y_1}{x_2-x_1}$

Finding slope from the given points :
$\text{Let,}{x}_1=-4,x_2=6y_1=-1,y_2=2slope=\left(\frac{2+1}{6+4}\right)$
= $\frac{3}{10}$ (i)
Now taking $x_1=6,x_2=3a{y}_1=2,y_2=a$
slope = ($\frac{a-2}{3a-6})$
= $\frac{a-2}{3a-6}$ (ii)
From the concept of collinearity
(i) = (ii)
$\frac{3}{10}$ = $\frac{a-2}{3a-6}$

$3\times (3a-6)=10\times (a-2)$
$(9a-18)=(10a-20)$
$-a=-2$
​​​​​​​$a=2$