Question

If the points $(a,-1),(2,1)$ and $(4,5)$ are collinear .Then ,the value of a is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is A $1$

Refer attached image.

Since the three points are on same line, so line equation formed by (2,1) , (4,5) satisfy equation of line given by:

$\frac{5-1}{4-2}=\frac{y-1}{x-2}$

$\Rightarrow \frac{4}{2}=\frac{y-1}{x-2}$

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

$\Rightarrow 2(x-2)=y-1$

$\Rightarrow 2x-4=y-1$

$\Rightarrow y=2x-3$ --Line Eqn --

Now put point (a-1) in Line Eqn

$-1=2a-3$

$\Rightarrow 2a=2$

$\therefore a=1$