Show that the following sets of points are collineara 2
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Show that the following sets of points are collinear.
(a) (2, 5) , (4, 6) and (8, 8)
(b) (1, -1), (2, 1) and (4, 5).
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Right Answer is:
SOLUTION
(a)
A (2 , 5) , B (4 , 6) and C (8 , 8) are the given points. Then, we have
AB=√(4−2)2+(6−5)2
AB=√4+1=√5
BC=√(8−4)2+(8−6)2
BC=√16+4=√20=2√5
and , AC=√(8−2)2+(8−5)2
AC=√36+9=√45=3√5
Clearly, AC = AB + BC
Hence A, B, C are collinear points
(b)
A (1 , -1) , B (5 , 2) and C (9 , 5) are the given points. Then, We have
AB=√(5−1)2+(2+1)2
AB=√16+9=5
BC=√(5−9)2+(2−5)2
BC=√16+9=5
and , AC=√(1−9)2+(−1−5)2
AC=√64+36=10
Clearly, AC = AB + BC
Hence A, B, C are collinear points