Question

If the points A(−1, −4), B(b, c) and C(5, −1) are collinear and 2b + c = 4, find the values of b and c.

Answer 1

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

∴ 1/2[x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂)] = 0
Here, x₁= −1 , y₁= −4, x₂= b, y₂= c, x₃= 5, y₃= −1

∴12[−1(c+1)+b(−1+4)+5(−4−c)]=0

⇒−c−1−b+4b−20−5c=0
⇒−6c+3b−21=0
⇒b−2c=7 ...(1)

Given:

2b+c=4 ...(2)

On solving equation (1) and (2), we get:

b=3 and c=−2