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

The sum of the lengths of any two line segments is equal to the length of the third line segment then all three points are collinear.

Let us assume

A = (1, 5) B = (2, 3) and C = (-2, -11)

Now let us find the distance between points.

Let us consider AB, BC and CA

AB= √[(2 – 1)2 + (3 – 5)2]

= √[(1)2 + (-2)2]

=√(1 + 4)

=√5

BC= √[(-2 – 2)2 + (-11 – 3)2]

= √[(-4)2 + (-14)2]

=√(16 + 196)

=√212

CA= √[(-2 – 1)2 + (-11 – 5)2]

= √[(-3)2 + (-16)2]

=√(9+ 256)

=√265

Since AB + BC ≠ CA

Hence, the points (1, 5), (2, 3), and ( – 2, – 11) are not collinear.

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