Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear

Solution:

Three or more points are said to be collinear if they lie on a straight line.

Let A(x₁, y₁) = (x, y),  B(x₂, y₂) = (1 , 2) and C(x₃, y₃) = (7, 0)

If the given points are collinear, then the area of triangle formed by these points will be 0.

Area of a triangle = 1/2 [x₁ (y₂ - y₃) + x₂ (y₃ - y₁) + x₃ (y₁ - y₂)] ....(1)

By substituting the values of vertices, A, B, C in the Equation (1),

Area = 1/2 [x(2 - 0) + 1(0 - y) + 7(y - 2)]

0 = 1/2 [2x - y + 7y - 14]

0 = 1/2 (2x + 6y - 14)

2x + 6y -14 = 0

x + 3y - 7 = 0

This is the required relation between x and y.

☛ Check: NCERT Solutions for Class 10 Maths Chapter 7

Video Solution:

Find a relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear.

Maths NCERT Solutions Class 10 Chapter 7 Exercise 7.4 Question 2

Summary:

A relation between x and y if the points (x, y), (1, 2) and (7, 0) are collinear is x + 3y - 7 = 0

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