Question

Plot the following points and check whether they are collinear or not (1,1), (2,3), (1,2)​

Answer 1

Answer:-

To check whether,

(1 , 1) & (2 , 3) & (1 , 2) are collinear points or not.

We know,

• When three points are collinear , then slope of first two points should be equal to Slope of next two points. i.e., If A , B , C are collinear points , Slope of AB = Slope of BC.

So,

Slope of a line joining the points (x₁ , y₁) , (x₂ , y₂) is ,

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

So,

Slope of (1 , 1) & (2 , 3) = (3 - 1)/(2 - 1)

• x₁ = 1
• y₁ = 1
• x₂ = 2
• y₂ = 3

⟹ m of (1 , 1) & (2 , 3) = 2/1

⟹ m of (1 , 1) & (2 , 3) = 2

Similarly,

m of (2 , 3) & (1 , 2) = (2 - 3)/(1 - 2)

⟹ m of (2 , 3) & (1 , 2) = - 1/ - 1

⟹ m of (2 , 3) & (1 , 2) = 1

We observe that,

Slope of (1 , 1) & (2 , 3) ≠ Slope of (2 , 3) & (1 , 2)

i.e., 2 ≠ 1.

Hence, The given points are not collinear.

Note : Collinear points are a certain number of points which lie on the same line.

Answer 2

$\bigstar {TO \: \: CHECK}$

$\bigstar{(1, 1) \: (2, 3) \: (1, 2) \: are \: collinear \: } \\ \\ { points \: or \: not \: .}</p><p>$

$\bigstar {When \: three \: points \: are \: collinear, \: } \\ \\ { then \: slope \: of \: first \: two \: points} \\ \\ { should \: be \: equal \: to \: Slope \: of \: next \: } \\ \\ {two \: points. \: i.e., \: If \: A, B, C \: are \: } \\ \\ {collinear \: points \: , Slope \: of \: } \\ \\ {AB = Slope \: of BC.}</p><p>$

$\\ \boxed{Slope (m) = \frac{y2 - y}{x2 - x} =}</p><p>$

$\\ \boxed{Slope \: of (1, 1) \: (2, 3) = \frac{3 - 2}{2 - 1} }$

$\\ \boxed{x = 1} \\ </p><p></p><p> \\ \boxed{y= 1} \\</p><p></p><p> \\ \boxed{x2 = 2}$