Question

If the points (1, 2), (-1, x) and (2, 3) are
collinear then the values of xis​

Answer 1

$\mathfrak{\pink{Answer:-}}$

Let the points A(1, 2), B(1, x) and C(2, 3) are collinear.

Area of triangle made by these points will be zero.

⇒1/2[x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)]

⇒ 1/2[(x – 3) + (-1)(3 – 2) + 2(2 – x)] = 0

⇒ x – 3 – 1 + 2(2 – x) = 0

⇒ x – 3 – 1 + 4 – 2x = 0

⇒ -x – 4 + 4 = 0

⇒ $\pink{\boxed{x = 0}}$

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