Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (A)

$1$

If three or more points lie on the same straight line then the points are collinear

Since, points lie on the same straight line, the area covered by them is zero.

Three points make a triangle. Therefore, the area of the triangle is zero

We know that area of the triangle is $\frac{1}{2}\left(x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right)$

Given collinear points are $(a,-1),(2,1),(4,5)$

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

$⟹a(1-5)+2(5-(-1\left)\right)+4(-1-1)=0$

$⟹-4a+12-8=0$

$⟹4a=4$

$⟹a=1$