Collinear Points Questions-5





In this page collinear points questions-5 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.



(A) Collinear
(B) Non Collinear




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.

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 (5,2) and B (3,-2) and C (8,8)

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

Here x₁ = 5, y₁ = 2, x₂ = 3  and  y₂ = -2

                             =    √(3-5))² + (-2-2)²

                       =    √(-2)² + (-4)²

                       =    √4 + 16

                       =    √20

                       =    √2 x 2 x 5 

                       =    2√5 units  

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

Here x₁ = 3, y₁ = -2, x₂ = 8  and  y₂ = 8

                             =    √(8-3)² + (8 -(-2))²

                       =    √(5)² + (8+2)²

                       =    √25 + 10²

                       =    √25 + 100

                       =    √125

                       =    √(5 x 5 x 5)

                       =    5 √5 units

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

Here x₁ = 8, y₁ = 8, x₂ = 5  and  y₂ = 2

                             =    √(5-8)² + (2-8)²

                       =    √(-3)² + (-6)²

                       =    √9 + 36

                       =    √45 

                       =    √3 x 3 x 5

                       =    3√5 units

AB = 2 √5 units

BC = 5 √5 units

CA = 3 √5 units

BC = AB + CA

5 √5  = 2 √5 + 3 √5

5 √5  = 5 √5

Therefore A,B and C are collinear.

This is the solution for collinear points questions-5.

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Collinear Points Question5 to Distance Between Two Points