Collinearity Of Points

To find the value of λ for which the points (2, -3), (λ, -1), and (0, 4) are collinear, we use the condition for collinearity that states if three points , , and are collinear, then the area of the triangle formed by these points is zero. The formula for the area of a triangle given three points is:

Substituting the given points (2, -3), (λ, -1), and (0, 4) into the formula:

Simplifying further:

For the area to be zero, the expression inside the absolute value must be zero:

Solving for λ:

Thus, the value of λ that makes the points collinear is .

The correct option is (C):0