Question

If points \( (5, 5) \), \( (10, k) \), and \( (-5, 1) \) are collinear, then the value of \( k \) is:

• A. 9
• B. 6
• C. 8
• D. 7

Hint:

For collinear points, equate the slopes between two pairs of points and solve for the unknown value.

Answer 1

The Correct Option is B

For three points to be collinear, the slopes between any two points must be equal. The slope between points \( (5, 5) \) and \( (-5, 1) \) is: \[ \text{slope} = \frac{1 - 5}{-5 - 5} = \frac{-4}{-10} = \frac{2}{5} \] The slope between points \( (5, 5) \) and \( (10, k) \) is: \[ \text{slope} = \frac{k - 5}{10 - 5} = \frac{k - 5}{5} \] Since the points are collinear, these two slopes must be equal: \[ \frac{k - 5}{5} = \frac{2}{5} \] Multiplying both sides by 5: \[ k - 5 = 2 \quad \Rightarrow \quad k = 7 \] Therefore, the correct answer is \( k = 7 \).