If the points \(X(2, -1), Y(3, k), Z(1, 4)\) are collinear, then the value of \(k\) is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → -6
Three points are collinear (on one straight line) when the line from X to Y has the same slope as the line from X to Z. The slope of the line through \((x_1,y_1)\) and \((x_2,y_2)\) is \(\frac{y_2-y_1}{x_2-x_1}\).
Slope of XY \(\displaystyle =\frac{k-(-1)}{3-2}=k+1\)
Slope of XZ \(\displaystyle =\frac{4-(-1)}{1-2}=\frac{5}{-1}=-5\)
\(k+1=-5\), so \(k=-6\)