Collinear Points Questions-2

In this page collinear points questions-2 we are going to see solution on the quiz.

Question 1 :

Examine whether the given points  A (3,7) and B (6,5) and C(15,-1) are collinear.

 (A) Collinear (B) Non Collinear

Question 2 :

Examine whether the given points  A (0,3) and B (1,5) and C (-1,1) are collinear.

Solution :

To show that the given points are collinear we need to find the distance between three points.

Distance Between Two Points (x ₁, y₁) and (x₂ , y₂)

√(x₂ - x₁) ² + (y₂ - y₁) ²

The three points are  A (0,3) and B (1,5) and C (-1,1)

Distance between the points A and B = √(x₂ - x₁) ² + (y₂ - y₁) ²

Here x₁ = 0, y₁ = 3, x₂ = 1  and  y₂ = 5

=    √(1-0)² + (5-3)²

=    √(1)² + (2)²

=    √1 + 4

=    √5 units

Distance between the points B and C = √(x₂ - x₁) ² + (y₂ - y₁) ²

Here x₁ = 1, y₁ = 5, x₂ = -1  and  y₂ = 1

=    √(-1-1)² + (1-5)²

=    √(-2)² + (-4)²

=    √4 + 16

=    √20

=    √(2 x 2 x 5)

=    2 √5 units

Distance between the points C and A = √(x₂ - x₁) ² + (y₂ - y₁) ²

Here x₁ = -1, y₁ = 1, x₂ = 0  and  y₂ = 3

=    √(0-(-1))² + (3-1)²

=    √(0+1)² + (2)²

=    √1² + 2²

=    √(1 + 4)

=    √5 units

AB = √5 units

BC = 2 √5 units

CA = √5 units

BC = AB + CA

2 √5  = √5 + √5

2 √5  = 2 √5

Therefore A,B and C are collinear.

This is the solution for collinear points questions-2.

Question 3 :

Examine whether the given points  A (1,4) and B (3,-2) and C (-3,16) are collinear.

 (A) Collinear (B) Non Collinear

Question 4 :

Examine whether the given points  A (1,4) and B (3,-2) and C (-3,16) are collinear.

 (A) Collinear (B) Non Collinear

Question 5 :

Examine whether the given points  A (5,2) and B (3,-2) and C (8,8) are collinear.

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 (A) Collinear (B) Non Collinear

Collinear Points Question2 to Distance Between Two Points