Question

state whether the following points are colinear or non colinear A(3,4),B(-2,-6),C(-1,-4)​

Answer 1

Answer:

Points A,B and C will be collinear if ar (ΔABC)=0

ar ΔABC=

2

1

[x

1

(y

2

−y

3

)+x

2

(y

3

−y

1

)+x

3

(y

1

−y

2

)]=0

⇒

2

1

[−6{6−(−8)}−4(−8−10)+3(10−6)]=0

⇒−6(14)−4(−18)+3(4)=0

⇒−84+84=0 , which is true

So , points A,B and C are collinear.

AC

2

=(x

2

−x

1

)

2

+(y

2

−y

1

)

2

=(3+6)

2

+(−8−10)

2

=81+324

⇒AC=

405

=9

5

units

AB

2

=[−4−(−6)

2

]+(6−10)

2

=(−4+6)

2

+(−4)

2

=(2)

2

+(−4)

2

=4+16

⇒AB

2

=20

⇒AB=2

5

units

Now , AB=

9

2

AC

R.H.S =

9

2

×9

5

=2

5

=AB

Hence , AB=

9

2

AC is true.