Question

If the points (3, 2) and (2, –3) are equidistant from points (x, y) show that x + 5y = 0

Answer 1

$atq \\ \sqrt{ {(x - 3)}^{2} + {(y - 2)}^{2} } = \sqrt{ {(x - 2)}^{2} + {(y + 3)}^{2} } \\ \sqrt{ {x}^{2} + 9 - 6x + {y}^{2} + 4 - 4y } = \sqrt{ { x }^{2} + 4 - 4x + {y}^{2} + 9 + 6y} \\ {x}^{2} + {y}^{2} - 6x - 4y + 13 = {x}^{2} + {y}^{2} - 4x + 6y + 13 \\ - 6x - 4y = - 4x + 6y \\ - 6x + 4x = 6y + 4y \\ - 2x = 10y \\ x = \frac{10y}{ - 2} \\ x = - 5y \\ x + 5y = 0 \\ hence \: proved.$