Question

If the points $(2,5),(4,6)$ and $(a,a)$ are collinear, then the value of $a$ is equal to

• A. $-8$
• B. $4$
• C. $-4$
• D. $8$

Answer 1

The correct option is D $8$

Consider the given points.

$(2,5),(4,6)$ and $(a,a)$

Since, these points are collinear means that the area of triangle must me zero.

So,

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

where $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ are the points

Therefore,

$2(6-a)+4(a-5)+a(5-6)=0$

$12-2a+4a-20+5a-6a=0$

$a-8=0$

$a=8$

Hence, this is the answer.