Question

if the distance between the points (a ,2 ) , (5, 1 ) is 5 unit .find the value of a

Answer 1

$d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } \\ {5}^{2} = {(5 - a)}^{2} + {(1 - 2)}^{2} \\ 25 = {(5 - a)}^{2} + 1 \\ 24 = {(5 - a)}^{2} \\ a = 5 - 2 \sqrt{6}$