If the distance between two points $(x, 7)$ and $(1, 15)$ is $10$ , find $x .$

7, - 5

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7, 5

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- 7, - 5

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None of these

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Solution

The correct option is B $7, - 5$
$(x, 7)$ and $(1, 15)$
Applying distance formula
$\sqrt{(1 - x)^{2} + (8)^{2}} = 10$
$1^{2} + x^{2} - 2 x + 64 = 100$
$x^{2} - 2 x - 35 = 0$
$x^{2} - 7 x + 5 x - 35 = 0$
$x (x + 5) - 7 (x + 5)$
$x = - 5$ or $7$

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