Question

a median OI
10. Find a relation between x and y, if the points A(2, 1), B(x, y) and C(7,5)
are collinear.
[CBSE 2009]​

Answer 1

Answer:

Points are A(2,1),B(x,y) and C(7,5) are collinear.

Which means area of triangle ABC=0

Area of a triangle=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

=

2

1

[2(y−5)+x(5−1)+7(1−y)]

=

2

1

[2y−10+4x+7−7y]

=

2

1

[4x−5y−3]

Since points are collinear:

2

1

(4x−5y−3)=0

4x−5y−3=0

Relationship between x and y.