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If p(x,y) is a point equidistance …

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If p(x,y) is a point equidistance from the points A(6,-1)and B(2,3)shoe thatx-y=3

Posted by Ashish Kumar 6 years, 4 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 4 months ago

Let A(6, -1) and B(2,3) be the given point and P(x,y) be the required point.

Since point P is equidistant from points A and B,therefore,
PA = PB {tex}\Rightarrow{/tex} (PA)² = (PB)²
{tex}\Rightarrow{/tex}(x - 6)² + (y + 1)² = (2 - x)² + (3 - y)²
{tex}\Rightarrow{/tex} 36 + x² - 12x + y² + 1 +2y = 4 + x² - 4x + 9 + y² - 6y
{tex}\Rightarrow{/tex} -12x + 4x + 2y + 6y = 4 + 9 - 1 - 36
{tex}\Rightarrow{/tex} -8x + 8y = -24
-8 (x - y)=-24
{tex}\Rightarrow{/tex} x - y = 3
Hence, x - y = 3

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