Question

Show that the points (1, 1), (2, 3) and (5, 9) are collinear.

Answer 1

Given: Points A(1, 1), B(2, 3) and C(5, 9).

`AB = sqrt((2 - 1)^2 + (3 - 1)^2` 

= `sqrt(1 + 4)`

= `sqrt(5)` 

`BC = sqrt((5 - 2)^2 + (9 - 3)^2` 

= `sqrt(9 + 36)`

= `sqrt(45)` 

= `3sqrt(5)`

`AC = sqrt((5 - 1)^2 + (9 - 1)^2` 

= `sqrt(16 + 64)`

= `sqrt(80)`

= `4sqrt(5)`

Now `AB + BC = sqrt(5) + 3sqrt(5)` 

= `4sqrt(5)` 

= AC

AB + BC = AC, so the three points A(1, 1), B(2, 3) and C(5, 9) are collinear.