Answer
$a\sqrt{2}$ units.
Work Step by Step
RECALL:
The distance $d$ between the points $(x_1, y_1)$ and $(x_2, y_2)$ can be found using the distance formula:
$d = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$
Use the formula above to obtain:
$d=\sqrt{(a-0)^2+(a-0)^2}
\\d=\sqrt{a^2+a^2}
\\d=\sqrt{2a^2}
\\d=\sqrt{a^2(2)}
\\d=a\sqrt{2}$
Thus, the distance between the two given points is $a\sqrt{2}$ units.