If the points \((1, -2)\), \((k, 2)\) and \((4, 10)\) are collinear, then the value of k is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2
Three points are collinear when the triangle they form has zero area:
\( \displaystyle \begin{vmatrix}1 & -2 & 1\\ k & 2 & 1\\ 4 & 10 & 1\end{vmatrix} = 0 \)
Expanding along the first row:
\(1(2 - 10) - (-2)(k - 4) + 1(10k - 8) = 0\)
\(-8 + 2k - 8 + 10k - 8 = 0\)
\(12k - 24 = 0\)
\(k = 2\)