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Question
If the sum of the distances of a moving point in a plane from the axes is 1, then find the locus of the point.
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Solution
Let coordinates of a moving point P be (x, y).
Given that the sum of the distances from the axes to the point is always 1
∴ |x| + |y| = 1
⇒ x + y = 1
⇒ – x – y = 1
⇒ – x + y = 1
⇒ x – y = 1
Hence, these equations gives us the locus of the point P which is a square.
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