Question

if the point A(-1,-4)B(b,c)and c(4,-1)are collinear and a-b=1find the values of a and b​

Answer 1

Answer:

If three points A,B,C are collinear 

Slope of AB = Slope of BC

Slope of AB =a+2b−1

Slope of AC =4+2−1−1=−32

Since A,B,C are collinear

a+2b−1=−32⇒3b−3+2a−4=0

3b+2a=7 ............. (1)

Given a−b=1⇒3a−3b=3 ........... (2)

Adding both (1) and (2), we get 

3b−3b+3a+2a=7+3

5a=10⇒a=2

Substituting it in equation (2), we get

2−b=1⇒b=1

Hence a=2,b=1.