Question

Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to ______.

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Answer 1

Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to 1.

Explanation:

As points are collinear

`\implies` Area of triangle formed by 3 points is zero.

`\implies 1/2|((x_1 - x_2)  (x_2 - x_3)),((y_1 - y_2)  (y_2 - y_3))| = 0`

`\implies 1/2|(((2x - 0),{0 - (x + 3)})),(((x + 3 - x),{x - (x + 6)}))| = 0` 

`\implies |(2x, -(x + 3)),(3, -6)| = 0` 

`\implies` –12x + 3(x + 3) = 0

`\implies` –12x + 3x + 9 = 0

`\implies` –9x = –9

`\implies` x = 1