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Is the point p(x,y) is equidistant …

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Is the point p(x,y) is equidistant pointA(5,1)B(_-1,5)prove that 3x=2y

    • Posted by Vishal Mani 6 years, 6 months ago

    CBSE > Class 10 > Mathematics
    • 1 answers

    Sia ? 6 years, 6 months ago

     The distances of P (x, y) from A (5,1) and B (-1,5) are equal, then we have to prove that 3x = 2y.

    PA = PB
    {tex}\therefore{/tex} PA2 = PB2
    By distance formula,
    (5 - x)2 + (1 - y)2= (-1 - x)2 + (5 - y)2
    {tex}\Rightarrow{/tex}25 - 10x + x2 + 1 - 2y + y2 = 1 + 2x + x2 + 25 - 10y + y2
    {tex}\Rightarrow{/tex} -10x - 2y = 2x - 10y
    {tex}\Rightarrow{/tex} 8y = 12x
    {tex}\Rightarrow{/tex}4(2y)= 4(3x)
    {tex}\Rightarrow{/tex}3x = 2y
    Hence Proved.

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