If the point P(x, y) is equidistant from A(5, 1) and B(-1, 5), th… - Vidyadip

MCQ

If the point $P(x, y)$ is equidistant from $A(5, 1)$ and $B(-1, 5),$ then

A
$5x = y$
B
$x = 5y$
✓
$3x = 2y$
D
$2x = 3y$

✓

Answer

Correct option: C.

$3x = 2y$

Points $P(x, y)$ is equidistant from $A(5, 1), B(-1, 5)$
then $AP = BP$
$ \Rightarrow AP^2= BP^2$
$ \Rightarrow(5-x)^2+(1-y)^2$
$=(-1-x)^2+(5-y)^2$
$ \Rightarrow 25+x^2-10 x+1+y^2-2 y$
$=1+x^2+2 x+25+y^2-10 y $
$\Rightarrow -10x - 2y + 26 = 2x - 10y + 26$
$\Rightarrow 2x + 10x = -2y + 10y$
$\Rightarrow 12x = 8y$
$\Rightarrow 3x = 2y$

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