Question

By distance formula prove that (-1,-1),(2,3)and(8,11)are collinear

Answer 1

For three points to be collinear, the sum of two side should be equal to third side.

So Here

A(-1,-1)

B(2,3)

C(8,11)

Then by distance formula,

AB = root{(2+1)2 +(3+1)2 }

AB =root(25)

AB =5

Similarly by distance formula we have,

BC=10

AC=15

Then,since AC is the longest .

BC + AB = 10 + 5 = 15 = AC

Hence AB + BC = AC

Hence the points are Collinear.

Answer 2

Step-by-step explanation:

A(-1,-1),B(2,3) ,C(8,11).

AB=√(2+1)^2+(3+1)^2

=√25

=5

BC=√(8-2)^2+(11-3)^2

=√36+64

=10

AC=√(-1-8)^2+(-1-11)^2

=√81+144

= 15

To prove this is collinear

AB+BC=AC only then this is a collinear

Here 5+10=15 ,so this is a collinear