Question

The distance between the points (2,-3) and (k,9) is 13units find k​

Answer 1

Step-by-step explanation:

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Answer 2

[HeY Mate]

$\huge\bold\blue{Answer}$

$distance \: formula => \sqrt{( x_{2} - x_{1} {}^{2} + (y_{2} - y_{1}) {}^{2} }$

Using distance formula,

$13 = \sqrt{(k - 2) {}^{2} + (9 + 3) {}^{2} } \\ 169 = k {}^{2} + 4 - 4k + 81 + 9 + 54 \\ 169 = k {}^{2} - 4k + 148 \\ k {}^{2} - 4k - 21 = 0 \\ k {}^{2} - (7 - 3)k - 21 = 0 \\ k {}^{2} - 7k + 3k - 21 = 0 \\ k(k - 7) + 3(k - 7) = 0 \\ (k - 7)(k + 3) = 0 \\ \\ k = + 7 \: or \: - 3$

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