## Collinear Points Questions-1

In this page collinear points questions-1, 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.

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 (3,7) and B (6,5) and C (15,-1)

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

Here x₁ = 3, y₁ = 7, x₂ = 6  and  y₂ = 5

=    √(6-3)² + (5-7)²

=    √(3)² + (-2)²

=    √9 + 4

=    √13 units

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

Here x₁ = 6, y₁ = 5, x₂ = 15  and  y₂ = -1

=    √(15-6)² + (-1-5)²

=    √(9)² + (-6)²

=    √81 + 36

=    √117

=    √(3 x 3 x 13)

=    3 √13 units

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

Here x₁ = 15, y₁ = -1, x₂ = 3  and  y₂ = 7

=    √(3-15)² + (7-(-1))²

=    √(-12)² + (7+1)²

=    √144 + 8²

=    √(144 + 64)

=    √208

=    √(2 x 2 x 2 x 2 x 13)

=    2 x 2 √13

=    4 √13 units

AB = √13 units

BC = 3 √13 units

CA = 4 √13 units

CA = AB + BC

4 √13  = √13 + 3 √13

4 √13  = 4 √13

Therefore A,B and C are collinear.

This is the solution for collinear points questions-1. 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.

 (A) Collinear (B) Non Collinear

Students can try to do the problems discussed above in this page 'collinear points questions-1' on their own. You can verify your solutions with the solutions given. Still if you are having any doubt you can contact us through mail, we will help you to clear your doubts.

Collinear Points Question1 to Distance Between Two Points 