Question

If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:

• A. 0
• B. \( \frac{1}{7} \)
• C. \( \frac{3}{10} \)
• D. \( \frac{7}{10} \)
• E. \( \frac{10}{7} \)

Hint:

To verify collinearity, equate the slopes between consecutive points and solve for unknown values.

Answer 1

Answer: (E)

Since the points are collinear, their slopes must be equal: \[ \frac{-1 + 3}{\lambda - 2} = \frac{4 + 3}{0 - 2} \] \[ \frac{2}{\lambda - 2} = -\frac{7}{2} \] Solving for \( \lambda \): \[ 4 = -7(\lambda - 2) \] \[ \lambda = \frac{10}{7} \]