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, that is, when this determinant is zero:
\( \begin{vmatrix}2&-3&1\\ \lambda&-1&1\\0&4&1\end{vmatrix} = 0 \)
Expanding along the first row:
\(2(-1 - 4) + 3(\lambda - 0) + 1(4\lambda - 0) = 0\)
\(-10 + 7\lambda = 0\)
\( \displaystyle \lambda = \frac{10}{7} \)