Question

If the points $(3,-2),(x,2)$ and $(8,8)$ are collinear find $10x$ using determinant.

Answer 1

$(3,-2),(x,2),(8,8)$ are collinear

$\therefore$ Area of triangle formed by point $=0$

$\frac{1}{2}\left|\begin{array}{ccc}3& -2& 1\\ x& 2& 1\\ 8& 8& 1\end{array}\right|=0$

$3(2-8)+2(x-8)+1(8x-16)=0$

$\left(3\right)(-4)+2x-16+8x-16=0$

$-12-16-16+10x=0$

$10x=44$

$x=4.4$