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Question
Show that the points (3, 4), (−5, 16) and (5, 1) are collinear.
Solution
Let the given points be A(3, 4), B(−5, 16) and C(5, 1).
Now,
\[\overrightarrow{AB} = \left[ \left( - 5 \hat{i} + 16 \hat{j} \right) - \left( 3 \hat{i} + 4 \hat{j} \right) \right] = - 8 \hat{i} + 12 \hat{j}\]
Clearly,
Therefore,
Hence, the given points (3, 4), (−5, 16) and (5, 1) are collinear.
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