Question

Determine whether the points A( 1, 2) , B( 5, 3), C(8, 6) are collinear.
​

Answer 1

Answer:

Given points are A(3,1),B(6,4) and C(8,6).

If AB+BC=AC, then the three points are collinear.

By distance formula, AB =

[(x

2

−x

1

)

2

+(y

2

−y

1

)

2

]

AB =

[(6−3)

2

+(4−1)

2

]

AB =

[(3)

2

+(3)

2

]

AB =

[9+9]

AB =

18

AB =

(9×2)

AB = 3

2

By distance formula, BC =

[(x

2

−x

1

)

2

+(y

2

−y

1

)

2

]

BC =

[(8−6)

2

+(6−4)

2

]

BC =

[(2)

2

+(2)

2

]

BC =

[4+4]

BC =

8

BC =

(4×2)

BC = 2

2

By distance formula, AC =

[(x

2

−x

1

)

2

+(y

2

−y

1

)

2

]

AC =

[(8−3)

2

+(6−1)

2

]

AC =

[(5)

2

+(5)

2

]

AC =

[25+25]

AC =

50

AC =

(25×2)

AC = 5

2

AB+BC = 3

2

+2

2

=5

2

= AC

Hence proved.

So A,B,C are collinear.