If the point \( \mathrm{A}(\mathrm{x}, \mathrm{y}) \) is equidistant from the points \( \mathrm{...

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If the point \( \mathrm{A}(\mathrm{x}, \mathrm{y}) \) is equidistant from the points \( \mathrm{B}(\mathrm{a}+\mathrm{b}, \mathrm{b}-\mathrm{a}) \) and \( \mathrm{C}(\mathrm{a}-\mathrm{b}, \mathrm{a}+\mathrm{b}) \), then prove that \( \mathrm{bx}=\mathrm{ay} \).
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