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

Let A = (1, 5), B = (2, 3) and C = (–2, –11)
Using Distance Formula to find distance AB, BC and CA.
AB = $$\sqrt{(2-1)^2 + (3 - 5)^2}$$
$$= \sqrt{1^2 - (-2)^2}$$
$$= \sqrt{1 + 5}$$
$$= \sqrt{5}$$
BC = $$\sqrt{(-2-2)^2 + (-11 - 3)^2}$$
$$= \sqrt{(-4)^2 - (-14)^2}$$
$$= \sqrt{16 + 196}$$
$$= \sqrt{212}$$
CA = $$\sqrt{(-2-1)^2 + (-11 - 5)^2}$$
$$= \sqrt{(-3)^2 - (-15)^2}$$
$$= \sqrt{9 + 256}$$
$$= \sqrt{265}$$
Since AB + AC $$\ne$$ BC, BC + AC $$\ne$$ AB and AC $$\ne$$ BC.
Therefore, the points A, B and C are not collinear.