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Question
Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.
Solution
Let the points (1, 5), (2, 3), and (−2, −11) be representing the vertices A, B, and C of the given triangle respectively.
Let A = (1,5), B = (2, 3), C = (-2, -11)
∴ `"AB" = sqrt((1-2)^2+(5-3)^2)`
`"BC" = sqrt((2-(-2))^2 + (3-(-11))^2)`
= `sqrt(4^2+14^2)`
= `sqrt(16+196)`
= `sqrt(212)`
= `2sqrt53`
CA = `sqrt((1-(-2))^2 + (5-(-11))^2)`
= `sqrt(3^2+16^2)`
= `sqrt(9+256)`
= `sqrt(265)`
Since AB + BC ≠ CA
Therefore, the points (1, 5), (2, 3), and (−2, −11) are not collinear.
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