Question

Find the value of x for which the points (x, −1), (2, 1) and (4, 5) are collinear ?

Answer 1

The points (x₁, y₁), (x₂, y₂) and (x₃, y₃) are collinear if `x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)`= 0 i.e., the area of triangle formed by the given points is zero.

Let the given points be A (x, − 1), B (2, 1) and C (4, 5).

The points A (x, − 1), B (2, 1) and C (4, 5) are collinear.

Therefore, Area of ΔABC = 0

`rArrx(1-5)+2[5-(-1)]+4(-1-1)=0`

`rArrx-4x+12-8=0`

`rArrx-4x+4=0`

`rArrx=1`

Thus, the value of x is 1.