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.