Question

If the points A(x,2) ,B(-3,-4) ,C(7,-5) are collinear then find the value of x.Reply fast

Answer 1

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Answer 2

You can use the formula for Area of triangle. When three points are collinear, The area formed by them is 0.

Therefore,
Area of triangle:
$\frac{1}{2} |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|$
Here The coordinates of the three points are (x1, y1), (x2, y2), (x3, y3).

Now plug the values and keep the area equal to 0.

$\frac{1}{2} |x( - 4 + 5) - 3( - 5 - 2) + 7(2 + 4)| = 0$
$|x + 21 + 42| = 0 \\ |x + 63| = 0 \\ x = - 63$