Question

If points \((1, 2), (x, -1), (4, 5)\) are collinear, then the value of \(x\) is

• A. -3
• B. -2
• C. 1
• D. 2

Hint:

Use the slope formula to check if points are collinear by setting the slopes equal to each other.

Answer 1

The Correct Option is C

To determine collinearity, the slope between the first two points must equal the slope between the second and third points. Using the slope formula: \[ \text{Slope between (1, 2) and (x, -1)} = \frac{-1 - 2}{x - 1} = \frac{-3}{x - 1} \] \[ \text{Slope between (x, -1) and (4, 5)} = \frac{5 - (-1)}{4 - x} = \frac{6}{4 - x} \] Equating the slopes: \[ \frac{-3}{x - 1} = \frac{6}{4 - x} \] Solving yields \(x = 1\). Therefore, the answer is 1.