Question

Find the value of x for which the points (x,-2), (2,4) and (-1,-5)
are collinear.​

Answer 1

Given:

• Points (x,-2), (2,4) and (-1,-5) are collinear.
• Area is therefore Zero

To Find:

• Find the value of x

Solution:

$Area = 0 \\ 0 = A= \frac{1}{2} |x1(y2−y3)+x2(y3−y1)+x3(y1−y2)|\\ 0 = \frac{1}{2} |x(4 + 5) + 2( - 5 + 2) + ( - 1)( - 2 - 4) | \\ 0 = |9x - 6 + 6| \\ 0 = 9x \\ \boxed{x = 0}$

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