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The points (0, 5), (0, –9) and (3, 6) are collinear. Is the following statement true or false

Solution:

Given, the points are (0, 5) (0, -9) and (3, 6).

We have to check if the points are collinear.

The area of a triangle with vertices A (x₁ , y₁) , B (x₂ , y₂) and C (x₃ , y₃) is

1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

To check for the points to be collinear, the area of the triangle must be zero.

Here, (x₁ , y₁) = (0, 5), (x₂ , y₂) = (0, -9) and (x₃ , y₃) = (3, 6)

Area of triangle = 1/2[0(-9 - 6) + 0(6 - (-9)) + 3(5 - (-9))

= 1/2[0 + 0 + 3(5 + 9)]

= 1/2[3(14)]

= 3(7)

= 21

Area of the triangle ≠ 0

Therefore, the given points are not collinear.

✦ Try This: Determine if the points (0, 4), (0, 4) and (5, 6) are collinear.

Given, the points are (0, 4) (0, 4) and (5, 6)

The area of a triangle with vertices A (x₁ , y₁) , B (x₂ , y₂) and C (x₃ , y₃) is

1/2[x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)]

To check for the points to be collinear, the area of the triangle must be zero.

Area of triangle = 1/2[0(4 - 6) + 0(6 - 4) + 5(4 - 4)

= 1/2[0 + 0 + 5(0)]

= 0

Area of triangle = 0

Therefore, the given points are collinear.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.2 Problem 3

The points (0, 5), (0, –9) and (3, 6) are collinear. Is the following statement true or false

Summary:

The statement “The points (0, 5), (0, –9) and (3, 6) are collinear” is false as it fails to satisfy the condition for collinearity. i.e. the area of the triangle joining the given points is not zero

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