Question

Determine if the points (1, 5), (2, 3) and (– 2, – 11) are collinear. class 10 maths exercises 7.1 3rd sum​

Answer 1

Answer:

CA=√257

Explanation:

A (1,5), B (2,3) and C (−2,−11)

Now,

AB = (1^2 )+(2^2 )= 5

BC = (4^2)+(14^2)

= √212

CA = (1^2)+(16^2)

= √257

As,CA>BC>AB

If points A,BandC are collinear then AB+BC=CA

But

=5+212

= 257

So they are not collinear.

Answer 2

Answer:

if points are collinear let say A=(1,5) B=(2,3) and C=(2, -11)

then

area formed by these points should be equals to zero

1/2*[x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)]=0

or, [x1(y2 - y3) + x2( y3 - y1)+ x3(y1 - y2)]=0

[1(3 - (-11)) + 2( (-11) - 5)+ (-2)(5 - 3)]

=42

not collinear

Explanation: