Question

The distance between the two points is (2,-3)and (k,9) is 13 units find k
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Answer 1

Explanation:

`\sqrt{(k - 2)^(2) + {(9 + 3)}^(2) } = 13 \\ \\ \therefore \: \sqrt{k^(2) - 2 * 2k + 2^(2) + {(12)}^(2) } = 13 \\ \\ \therefore \: \sqrt{k^(2) - 4k + 4 + 144 } = 13\\ \\ \therefore \: \sqrt{k^(2) - 4k + 148 } = 13 \: \\ \: \: \: \: \: \: squaring \: both \: sides \\ \\ k^(2) - 4k + 148 = 169 \\ \\ \therefore \: k^(2) - 4k + 148 - 169 = 0\\ \\ \therefore \: k^(2) - 4k - 21 = 0\\ \\ \therefore \: k^(2) - 7k + 3k - 21 = 0\\ \\ \therefore \: k(k - 7) + 3(k - 7) = 0 \\ \\ \therefore \: (k - 7) (k+ 3) = 0 \\ \\ \therefore \: (k - 7) = 0 \: or \: (k+ 3) = 0 \\ \\ \therefore \: k = 7 \: or \: k = - 3 \\ \\ \huge \purple{ \boxed{\therefore \:k = \{ - 3, \: \: 7 \}}}`