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If the point P(x,y) is equidistant …

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If the point P(x,y) is equidistant from the points A(5,1) and B(1,5), prove that x=y.

Posted by Diksha Dabas 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

PA = PB (Given)
{tex}\therefore {/tex} PA² = PB²
{tex} \Rightarrow {/tex} (5 - x)² + (1 - y)² = (1 - x)² + (5 - y)²
{tex} \Rightarrow {/tex} 25 + x² - 10x + 1 + y² - 2y = 1 + x² - 2x + 25 + y² - 10y
{tex} \Rightarrow {/tex} -8x = -10y + 2y
{tex} \Rightarrow {/tex} -8x = -8y
{tex} \Rightarrow {/tex} x = y

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CBSE > Class 10 > Mathematics