Question

If the points $(2,5),(4,6)$ and $(a,a)$ are collinear, then find the value of ${}^{\prime }{a}^{\prime }$

• A. $4$
• B. $-4$
• C. $-8$
• D. $8$

Answer 1

Answer: (D)

$8$

Given the points $(2,5),(4,6)$ and $(a,a)$ are collinear. Then the area of the triangle formed by the points is $0$.

Then we have,

$\left|\begin{array}{ccc}1& 2& 5\\ 1& 4& 6\\ 1& a& a\end{array}\right|=0$

or, $\left|\begin{array}{ccc}1& 2& 5\\ 0& 2& 1\\ 0& a-2& a-5\end{array}\right|=0$ [ $R_2^{\prime }=R_2-R_1$ and $R_3^{\prime }=R_3-R_1$]

or, $2(a-5)-(a-2)=0$

or, $a-8=0$

or, $a=8$.