The points (2, –3), (4, 3) and are on the same straight line. The value(s) of k is (are):

Engineering

Mathematics

Locus of a Point

Various Form of a Straight Line

Question

The points (2, –3), (4, 3) and $(5, \frac{k}{2})$ are on the same straight line. The value(s) of k is (are):

– 12

± 12

12 or 6

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Given (2, –3), (4, 3) and $(5, \frac{k}{2})$ are on same straight line.

∴ \frac{3 - (- 3)}{4 - 2} = \frac{\frac{k}{2} - 3}{5 - 4} ⟹ \frac{6}{2} = \frac{\frac{k}{2} - 3}{1} ⟹ 3 = \frac{k}{2} - 3

∴ k = 12