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show that the points (1 ,7) …

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show that the points (1 ,7) (4, 2) (-1, -1) and(-4 ,4 )are the vertices of a square

    • Posted by Yash Sonawane 6 years, 11 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Yogita Ingle 6 years, 11 months ago

    Let the given vertices be A (1,7), B (4,2), C (-1,-1), D (-4,4)
    AB = √ (4-1)2 + (2 -7)2 = √ 9 + 25 = √  34
    BC = √ (-1-4)2 + (-1-2)2 = √ 25 + 9 = √ 34
    CD = √ (-4+1)2 + (4 +1)2 = √  9 + 25 = √ 34
    AD = √ (1 +4)2 + (7 -4)2 = √ 25 + 9 = √ 34
    AC = √ (-1-1)2 + (-1-7)2 = √ 4 + 64 = √ 68
    BD = √ (-4-4)2 + (4 - 2)2 = √  64 + 4 = √ 68
    Clearly, AB = BC = CD = DA and AC = BD
    Hence, given points are the vertices of a square

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