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Write the coordinates of a point …

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Write the coordinates of a point P on x- axis which is equidistant from the points A(-2,0) and B(6,0).

Posted by Priyanshi Jain 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Point P(x, 0) is equidistant from point A(- 2, 0) and B(6, 0) i.e. AP = BP

{tex}\Rightarrow AP^2=BP^2{/tex}

{tex}\Rightarrow (-2-x)^2+(0-0)^2=(6-x)^2+ (0-0)^2{/tex}(by distance formula)

{tex}\Rightarrow [(-1)(2+x)]^2=(6-x)^2{/tex}

{tex}\Rightarrow 4+4x+x^2=36- 12x +x^2{/tex}

{tex}\Rightarrow 4+4x=36- 12x {/tex}

{tex}\Rightarrow 36- 12x -4-4x=0{/tex}

{tex}\Rightarrow 32- 16x =0{/tex}

{tex}\Rightarrow 32= 16x {/tex}

{tex}\Rightarrow x=2{/tex}

Hence, point P(2,0) is equidistant from point A(- 2, 0) and B(6, 0).

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