Question

determine os valores  de k sabendo que a distancia entre as coordenadas A (4;0) e B (1;k) é igual a 5.

Answer 1

$d = \sqrt{ (x_a-x_b)^2+(y_a-y_b)^2 } \\\\\ 5 = \sqrt{ (4-1)^2+(0-k)^2 } \\\\ 5 = \sqrt{ (3)^2+(-k)^2 } \\\\\ 5 = \sqrt{ 9+k^2 } \\\\\ (5)^2 = ( \sqrt{ 9+k^2 })^2\\\\\ 25=9+k^2\\\\ k^2=25-9\\\\\ k^2=16\\\\ \boxed{k=4}$