The points (K, 3), (2, -4) and (-k + 1, -2) are collinear. Find K.

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Solution

Given, points A (K, 3), B (2, -4) and C (-K + 1, -2) are collinear.

Slope of AB = Slope of BC

$fraction numerator negative 4 minus 3 over denominator 2 minus k end fraction equals fraction numerator negative 2 plus 4 over denominator negative k plus 1 minus 2 end fraction fraction numerator negative 7 over denominator 2 minus k end fraction equals fraction numerator 2 over denominator negative k minus 1 end fraction 7 k plus 7 equals 4 minus 2 k 9 k equals negative 3 k equals fraction numerator negative 1 over denominator 3 end fraction$

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