Question

For what value of k the distance between points (5, -2) and (k,4) is 10

Answer 1

I hope you understand.....

Answer 2

Distance formula=

$\sqrt{( x_{2} - x_{1})^{2} + ( y_{2} - y_{1})^{2} }$

Here,

$\: \sqrt{( k- 5)^{2} + (4 - ( - 2))^{2}} = 10 \\ ( k- 5)^{2} + (4 - ( - 2))^{2} = 100 \\ k^{2} + 25 - 10k \: + 36 = 100 \\ {k}^{2} - 10k - 39 = 0$

So k = 13 or k = -3