Question

Show that the points ( 3, -2), ( 1, 4) and ( -1, 10) are collinear.

Answer 1

Let A( 3, -2 ), B( 1, 4 ), C( -1, 10 ).

Using distance formula,

AB = √{(3-1)² + (-2-4)²}

= √{4+36}

= √40

= 2√10

similarly,

BC = √{4+36}

= 2√10

AC = √{16+144}

= √160

= 4√10

AC = AB+BC

If 3 points are collinear, the on finding the distances between them, the largest distance should be sum of other 3 distances.

So, here A, B, C are collinear.

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Answer 2

Your solution is in above pic.