Question

Find the value of x,so that the points (1,-5),(-4,5) and (×,7) are collinear.

Answer 1

Answer:

-5

If the points are collinear then they will form no triangle means area of triangle formed by them is equals to zero.

As we know that area of triangle found by three coordinates is given by

$\frac{1}{2} \times | x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)</p><p>|$

as the given points are collinear to area of triangle formed by these points is equals to zero

So,

$\frac{1}{2} \times |1(5 - 7) + ( - 4)(7 + 5) + x( - 5 - 5)| = 0 \\ \implies | - 2 - 48 - 10x| = 0 \\ \implies \: 10x + 50 = 0 \\ \implies \: x = - 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \boxed{ \underline{ Answer }}}$

hence final value of x is -5