Question

If the points A(x 2) ,B(-3 -4) ,C(7,-5) are collinear then find the value of x

Answer 1

Answer:

We know the points are collinear if area (ΔABC)=0

Area of triangle =

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]

Then, Area =

2

1

{a(b

1

−(b−b

1

)+a

1

{(b−b

1

)−b}+(a−a

1

)(b−b

1

)}=0

2

1

{ab

1

−(ab−ab

1

)+a

1

b−a

1

b

1

−a

1

b}+(ab−ab

1

−a

1

b+a

1

b

1

)=0

{ab+a

1

b

1

}=ab−ab

1

−a

1

b+a

1

b

1

−ab

1

−a

1

b=0

−ab

1

=a

1

b

Therefore, We can write as

a

1

a

=

b

1

b

Hence, proved.

Answered By