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.