Verify whether point P(6, −6), Q(3, -7), and R(3, 3) are collinear.
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Answered by
2
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
Answered by
3
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!!!
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