Question

If the points $(6,9),(10,x)$ and $(-6,-7)$ are collinear then find the value of $x$.

Answer 1

Consider the following question.

Let A,B & C are collinear.

$A(6,9)B(10,x)\&C(-6,-7)$

Hence,

Slope of AB=Slope of BC

$\frac{x-9}{10-6}=\frac{-7-x}{-6-10}$

$\frac{x-9}{10-6}=\frac{7+x}{6+10}$

$\frac{x-9}{4}=\frac{7+x}{16}$

$x=\frac{43}{3}$

Hence, this is the required answer.