Question

Plzz ans it fast.. i need it

Answer 1

That has to be the way you r looking for.

Answer 2

Ist approach:-

(4,-5), (1,1), (-2,7),

Let A, B and C be the position of these three co-ordnates,

So now if A,B and C are the collinear then

AB=√[(1+5)²+(1-4)²],

AB=√[(6)²+(-3)²],

AB=√(36+9)=√45=3√5,

BC=√[(7-1)²+(-2-1)²],

BC=√[(6)²+(-3)²],

BC=√(36+9)=√45=3√5,

AC=√[(7+5)²+(-2-4)²],

AC=√[(12)²+(-6)²],

AC=√(144+36)=√180,

AC=√(6×6×5)=6√5,

therefore

AB+BC=3√5+3√5=6√5=AC,

then

A,B and C will be collinear points.


IInd approach:-

If slope of AB = slope of BC,

then

A, B and C will be the collinear points,

then

Slope of AB =(1+5)/(1-4),

=6/-3 = -2,

now
Slope of BC = (7-1)/(-2-1),

=6/-3 = -2,

Since slopes are equal then A, B and C will be collinear.

IIIrd approach:-


Just find the equation of line passing through two points using

(y-y1) = (y2-y1)/(x2-x1) ( x-x1),

and after getting the equation of this particular line just put remaining coordinates of the point in the equation of line if given points are collinear then the remaining points satisfied the equation of the line.


IVth approach:-


If points are collinear then area of traingle will be zero mean no triangle will be formed so just use the formula of area of traingle you can easily prove it.

Area of ∆ = 1/2 [x1(y2-y3)+x2(y3-y1)+x3(y1-y2)],



need one more approach????
then you can also solve it using mattrix