Question

A and B are points on the line x + y = a lying on the coordinate axis. If AB = 5 $\sqrt{2}$, find the coordinates of A and B, given that A and B are equidistant from the origin.

Answer 1

Since A and B lie on the line x + y = a, the coordinates of these points satisfy the relation x + y = a
So, let O be the origin, since OA = OB, let A = (0,a) and since A and B are equidistant from O(0,0), coordinates of B are (a,0)
In right angled triangle AOB, ${AB}^2$ = ${AO}^2$ + ${BO}^2$ = 2 $a^2$. So, AB = a $\sqrt{2}$
= 5 $\sqrt{2}$. So a = 5

Answers: (0,5) ; (5,0)