Q. 165.0( 3 Votes )

# If the points A(-

Answer :

Given points A(-2, 1), B(a, b) and C(4, -1) are collinear

And a – b = 1 …(1)

We have to find the values of a and b.

Since the given points are collinear, the area of the triangle formed by them must be 0.

We know that the area of Triangle =  [x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = 0

[-2(b – (-1)) + a(-1 – 1) + 4(1 – b)] = 0

[-2(b + 1) -2a + 4(1 – b)] = 0

[-2b -2 -2a + 4 – 4b] = 0

-2a - 6b + 2 = 0

-2a – 6b = -2

Dividing by -2, we get

a + 3b = 1

a = 1- 3b … (2)

Substituting (2) in (1),

(1 – 3b) – b = 1

1 – 4b = 1

4b = 0

b = 0

Substituting value of b in (1),

a - 0 = 1

a = 1

Ans. The values of a and b are 1 and 0 respectively.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses 