# 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 single straight line.

Let A(x_{1}, y_{1}) = (x, y), B(x_{2},y_{2}) = (1 , 2) and C(x_{3},y_{3}) = (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 {x_{1} (y_{2} - y_{3}) + x_{2} (y_{3}- y_{1}) + x_{3} (y_{1} - y_{2})} ....Equation(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.

**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:

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

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