Collinearity Of Points

Step 1: Recall the condition for collinearity of three points.

Three points , , and are collinear if the area of the triangle formed by them is zero. The formula for the area of a triangle is:

For collinearity, the area must be zero:

Step 2: Substitute the coordinates of the given points.

The points are , , and . Substituting into the collinearity condition:

Simplify each term:

Step 3: Solve for .

Final Answer: The value of is , which corresponds to option .

Given points: , , and

Step 1: Condition for collinearity

Three points are collinear if the area of the triangle they form is zero.

The area of a triangle formed by three points , , and is given by:

Step 2: Substitute given points

Step 3: Solve for

Final Answer: 1

If three points , , and are collinear, the area of the triangle formed by these points is zero. The area of the triangle is given by: $ (x_1, y_1) = (1, 2) (x_2, y_2) = (-1, k) (x_3, y_3) = (2, 3) $