Question

Verify whether the points (-2,3), (4,2) and (10,1) are collinear or not.

​

Answer 1

Step-by-step explanation:

Given points (1,5),(2,3)(−2,−1)

Lets find a equation of line passing through (1,5)(2,3)

→

x−1

y−5

=

3−5

2−1

→−2(y−5)=x−1

→−2y+10=x−1

→x+2y=11

Point (−2,−1)⇒−2+2(−1)=−4



=11

So, point (−2,−1) do uot passes through line all thsee points are not collinear.

Answer 2

If they are collinear they must have same slope(or you can say, they lie on the same line).

Slope of (-2, 3) and (4,2)= (y₂ - y₁)/(x₂ - x₁)

              ⇒ (3 - 2)/(-2 - 4)

              ⇒ - 1/6

Slope of (-2, 3) and (10,1)= (y₂ - y₁)/(x₂ - x₁)

              ⇒ (3 - 1)/(- 2 - 10)

              ⇒ 2/(-12)

              ⇒ - 1/6

As both are same, they are collinear.