Question

If the points (1, 2), (-1, k) and (2, 3) are collinear, then the value of k is

• A. 0
• B. -1
• C. 1
• D. 2

Answer 1

The Correct Option is A

If three points $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ are collinear, the area of the triangle formed by these points is zero. The area of the triangle is given by: $$\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| = 0$$ Here, $(x_1, y_1) = (1, 2)$, $(x_2, y_2) = (-1, k)$, and $(x_3, y_3) = (2, 3)$. So, $$\frac{1}{2} |1(k - 3) + (-1)(3 - 2) + 2(2 - k)| = 0$$ $$|k - 3 - 1 + 4 - 2k| = 0$$ $$|-k| = 0$$ $$k = 0$$