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