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If the point p(x,y)is equidistant from …

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If the point p(x,y)is equidistant from the point a(1,5) and b(5,1)then prove that x=y

Posted by Sanchit Kalkal 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Given , point P(x,y) is equidistant from points L(5,1) = (x₁, y₁) and M(-1,5)= (x₂, y₂).
So, PL = PM

{tex}\Rightarrow PL^2=PM^2{/tex} [On squaring both sides]
{tex}\Rightarrow\left(\sqrt{{(x_\;\;-x_1)}^2+\;(y\;-y_1)^2}\right)^2\;=\;\left(\sqrt{{(x\;-x_2)}^2+\;(y\;\;-y_2)^2}\right)^2{/tex}

{tex}\Rightarrow (x-5)^2+(y-1)^2=(x+1)^2+(y-5)^2{/tex} [Using distance formula]
⇒ x² - 10x + 25 + y² - 2y + 1 = x² + 2x + 1 + y² - 10y + 25
⇒ - 10x - 2y + 26 = 2x - 10y + 26
⇒ -10x - 2x = - 10y + 2y
⇒ - 12 x = - 8y
{tex}\Rightarrow 3x=2y{/tex}

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CBSE > Class 10 > Mathematics