# If the points <sp

Given points A(-1, -4), B(b, c) and C(5, -1) are collinear

And 2b + c = 4 … (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 =

= 0

[x1(y2 – y3) + x2(y3 – y1) + x3(y1 – y2)] = 0

[-1(c – (-1)) + b(-1 – (-4)) + 5(-4 – c)] = 0

[-1(c + 1) + 3b + 5(-4 – c)] = 0

[-c - 1 + 3b - 20 – 5c] = 0

3b – 6c - 21 = 0

3b – 6c = 21

Dividing by 3, we get

b – 2c = 7

b = 7 + 2c … (2)

Substituting (2) in (1),

2(7 + 2c) + c = 4

14 + 4c + c = 4

5c = -10

c = -2

Substituting value of c in (1),

2b + (-2) = 4

2b = 6

b = 3

The values of a and b are 3 and -2 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