Question

Find the value of k for which the distance between the point (4,k) (1,0) is 5

Answer 1

use distance formula
(4-1)^2 + k^2 = 25
9 + k^2= 25
k^2 = 16
k= 4

Answer 2

$STRAIGHT \: \: LINES \\ \\ \\ \:using \: distance \: formula \: - \\ \\ 5 = \sqrt{ {(4 - 1)}^{2} + {(k - 0)}^{2} } \\ \\ squaring \: both \: sides \: \\ we \: get \: - \\ \\ 25 = {3}^{2} \: + {k}^{2} \: \: \\ \\ 25 = 9 + {k}^{2} \\ \\ {k}^{2} = 16 \\ \\ k = 4 \: \: \: \: \: \: or \: \: \: \: \: \: \: k = - 4 \: \: \: \: \: ans.$