If the points, (2, −3), \((\lambda, -1)\) and (0, 4) are collinear, then the value of \(\lambda\) is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{10}{7}\)
Three points are collinear when the triangle they form has zero area:
\( \displaystyle \frac{1}{2}\begin{vmatrix} 2 & -3 & 1 \\ \lambda & -1 & 1 \\ 0 & 4 & 1 \end{vmatrix} = 0 \)
Expanding along the first row:
\(2(-1 - 4) + 3(\lambda - 0) + 1(4\lambda - 0) = 0\)
\(-10 + 3\lambda + 4\lambda = 0\)
\(7\lambda = 10\)
\( \displaystyle \lambda = \frac{10}{7} \)