Answer:
k = - 11, 5
Step-by-step explanation:
By distance formula:
[tex] \sqrt{ \{ {k - ( - 3) \}}^{2} + \{5 - ( - 1) \}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + {(5 + 1)}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + {(6)}^{2} } = 10 \\ \\ \sqrt{ {(k + 3)}^{2} + 36 } = 10 \\ \\ (k + 3)^{2} + 36 = {10}^{2} \\ ..(squaring \: both \: sides) \\ {k}^{2} + 6k + 9 + 36 = 100 \\ {k}^{2} + 6k + 45 - 100 = 0 \\ {k}^{2} + 6k - 55 = 0 \\ {k}^{2} + 11k - 5k - 55 = 0 \\ k(k + 11) - 5(k + 11) = 0 \\ (k + 11)(k - 5) = 0 \\ k + 11 = 0 \: or \: k - 5 = 0 \\ k = - 11 \: or \: k = 5 \\ \\ \huge \red { \boxed{k = \{ - 11, \: 5\}}}[/tex]
