Question

Verify whether point P(6, −6), Q(3, -7), and R(3, 3) are collinear.​

Answer 1

When three points are collinear, the area of triangle will be 0

area of triangle = 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)

1/2( 6(-7-3) + 3(3+6) + 3(-6+7) = 0

1/2(6×-10 + 3×9 + 3×1)= 0

(-60 + 27 + 3)= 0

-15 is not equal to 0

hence they are not collinear

Answer 2

Answer:

P,Q,R are not collinear!!!

Step-by-step explanation:

If P,Q,R lie on same line then

Point R will lie on line PQ

Slope of PQ = y2 -y1/ x2 - x1

=-7-(-6)/3-6

=-1/-3

m = 1/3

therefore Eq of line PQ=  

(y-y1)=m(x-x1)

(y-(-6))=(1/3)(x-6)

(y+6)=(x-6)/3

3y+18=x-6

3y-x+24=0

Equation of PQ=

3y-x+24=0

R must lie on equation of line PQ

therefore substituting coordinates of R in eq PQ

put, x= 3

put, y=3

L.H.S.= 3y-x+24

= 3(3)-3+24

=9-3+24

=6+24

=30

which is not equal to 0

therefore

P,Q,R are not collinear!!!