determine if the points (2,-1) ,(1,-4) ,and (3,2) are collinear
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Answer:
The given points are A(1,5), B(2,3) and C(−2,−11).
Let us calculate the distance : AB, BC and CA by using distance formula.
AB=
(2−1)
2
+(3−5)
2
=
(1)
2
+(−2)
2
=
1+4
=
5
units
BC=
(−2−2)
2
+(−11−3)
2
=
(−4)
2
+(−14)
2
=
16+196
=
212
=2
53
units
CA=
(−2−1)
2
+(−11−5)
2
=
(−3)
2
+(−16)
2
=
9+256
=
265
=
5
×
53
units
From the above we see that : AB+BC
=CA
Hence, the above stated points A(1,5), B(2,3) and C(−2,−11) are not collinear.
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