Question

Determine if the points (1, 5), (2, 3) and (−2, −11) are collinear.

Answer 1

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.