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.