86.7k views
0 votes
Find the equation of line passing through the points A(-1,3) and B(0,2). Hence show that the points A,B and C (1,-1) are collinear.

User Masuri
by
8.1k points

1 Answer

2 votes

Given:

A line passes through A( - 1 , 3) & B(0 , 2).

Prove:

A , B , C(1 , 1) are collinear.

Proof:

We know that,

Slope of a line passing through the co - ordinates (x₁, y₁) and (x₂ , y₂) is :

m = (y₂ - y₁)/(x₂ - x₁)

Let,

  • x₁ = - 1
  • x₂ = 0
  • y₁ = 3
  • y₂ = 2

Hence,

→ m = (2 - 3)/( 0 - ( - 1))

→ m = - 1/1

→ m = - 1

Now,

Equation of a line ⟹ y - y₁ = m (x - x₁)

Putting the values we get,

→ y - 3 = - 1(x - ( - 1))

→ y - 3 = - x - 1

→ y + x = - 1 + 3

→ x + y = 2

Hence, the equation of the line is x + y = 2.

Now,

we have to prove that,

A , B , C are collinear.

  • If three points are collinear then the area of the triangle formed by them will be zero.
  • Three points are collinear if the slope of line passing through the line segment are equal.

i.e.,

Slope of AB should be equal to Slope of BC.

We have;

Slope of AB = - 1.

→ - 1 = ( 1 - 2)/(1 - 0)

→ - 1 = - 1/1

→ - 1 = - 1

Hence, A , B , C are collinear points.

I hope it will help you.

Regards.

User Omoro
by
7.9k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories