If the point (, ) is equidistant from the points ( + , − ) and ( − , + ), then prove that = .

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If the point 𝑃(𝑥, 𝑦) is equidistant from the points 𝑄(𝑎 + 𝑏, 𝑏 − 𝑎) and 𝑅(𝑎 − 𝑏, 𝑎 + 𝑏), then prove that 𝑏𝑥 = 𝑎𝑦.

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It has been given that the point 𝑃(𝑥, 𝑦) is equidistant from the points 𝑄(𝑎 + 𝑏, 𝑏 − 𝑎) and 𝑅(𝑎 − 𝑏, 𝑎 + 𝑏), and we need to prove that 𝑏𝑥 = 𝑎𝑦..

We know that, distance between two points 𝑃 and 𝑄 are calculated by

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