Question

Q. 22. Which point on x-axis is equidistant from (7, 6) and (-3, 4) ?
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Answer 1

Answer:

$point \: \: is \: \: \: (3 \: \: \: \: \: \: 0)$

Step-by-step explanation:

$\sqrt{ {(x - 7)}^{2} + {(y - 6)}^{2} } = \sqrt{ {(x + 3)}^{2} + {(y - 4)}^{2} } \\ \\ \\ {(x - 7)}^{2} - {(x + 3)}^{2} = {(y - 4)}^{2} - {(y - 6)}^{2} \\ \\ \\ (x - 7 - x - 3)(x - 7 + x + 3) = (y - 4 - y + 6)(y - 4 + y - 6) \\ \\ ( - 10)(2x - 4) = 2(2y - 10) \\ \\ - 5(x - 2) = (y - 5) \\ \\ y - 5 + 5x - 10 = 0 \\ \\ 5x + y - 15 = 0 \\ \\ 5x + y = 15 \: \: \: \: on \: x \: \: axis \\ \\ \\ y = 0 \\ \\ \\ therefore \: \: \: 5x = 15 \\ \\ x = 3 \\ \\ \\ point \: \: is \: \: \: (3 \: \: \: \: \: \: 0)$