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Question
Show that the points (0, 0), (5, 3) and (10, 6) are collinear.
Sum
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Solution
Given: Let A = (0, 0), B = (5, 3), C = (10, 6).
`AB = sqrt((5 - 0)^2 + (3 - 0)^2`
= `sqrt(25 + 9)`
= `sqrt(34)`
`BC = sqrt((10 - 5)^2 + (6 - 3)^2`
= `sqrt(25 + 9)`
= `sqrt(34)`
`AC = sqrt((10 - 0)^2 + (6 - 0)^2`
= `sqrt(100 + 36)`
= `sqrt(136)`
= `2 · sqrt(34)`
Therefore, `AB + BC = sqrt(34) + sqrt(34)`
= `2 · sqrt(34)`
= AC
Since AB + BC = AC, the points (0, 0), (5, 3) and (10, 6) are collinear.
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