# Find a Relation Between X and Y, If the Points A(X, Y), B(-5, 7) and C(-4, 5) Are Collinear. - Mathematics

Find a relation between x and y, if the points A(x, y), B(-5, 7) and C(-4, 5) are collinear.

#### Solution

Let A(x_1=x,y_1=y),B(x_2=-5,y_2=7) and C (x_3 =-4, y_3=5) be the given points

The given points are collinear if

x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0

⇒ x(7-5)+(-5)(5-y)+(-4)(y-7)=0

⇒7x-5x-25+5y-4y+28=0

⇒ 2x +y+3=0

Hence, the required relation is 2x +y+3 =0

Concept: Area of a Triangle
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#### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths
Chapter 16 Coordinate Geomentry
Q 20