Question

13 is the distance between the points (x,15) and (4,3) find x

Answer 1

Given : 13 units is the distance between the points (x , 15) and (4 , 3).

To Find : Value of x.

Formula used :

$\star \: \underline{\boxed{\bold\purple{ distance = \sqrt{ (x_{2} - x_{1}) } {}^{2} + \sqrt{ (y_{2} - y_{1}) } {}^{2}}}}$

Solution :

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$\large:\implies \sf \: 13 = \sqrt{(4 - x) {}^{2} + (3 - 15) {}^{2} } \\ \\ \\ \large:\implies \sf \: 13 =(4 - x) + (3 - 15) \\ \\ \\ \large:\implies \sf \: 13 = 4 - x + 3 - 15 \\ \\ \\ \large:\implies \sf \: 13 = - 12 + 4 - x \\ \\ \\ \large:\implies \sf \: 13 = - 8 - x \\ \\ \\ \large:\implies \sf \: x = - 8 - 13 \\ \\ \\ \large:\implies \sf \: \underline{\boxed{\sf\pink{x = - 21}}} \: \bigstar$

$\sf\therefore Hence, the \: value \: of \: x \: is \: \bold{-21}.$