Question

answer this question

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Answer 1

Answer:

$d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ \\ d = \sqrt{ {( \frac{ {2t}^{2} }{ 1 + {t}^{2} } - 1) }^{2} + ( \frac{1 - {t}^{2} }{1 + {t}^{2} } - 1) {}^{2} } \\ \\ = \sqrt{ (\frac{2 {t}^{2} - 1 - {t}^{2}) {}^{2} + (1 - {t}^{2} - 1 - {t}^{2}) {}^{2} }{(1 + {t}^{2} ) {}^{2} } } \\ \\ = \sqrt{ \frac{( {t}^{2} - 1) {}^{2} + ( - 2 {t}^{2}) {}^{2} }{(1 + {t}^{2}) {}^{2} } } \\ \\ = \frac{ \sqrt{ {t}^{4} - 2 {t}^{2} + 1 + 4t {}^{4} } }{1 + {t}^{2} } \\ \\ = \frac{ \sqrt{5 {t}^{4} - 2 {t}^{2} - 1 } }{1 + {t}^{2} }$