Answer
$ a.\qquad$ The distances are equal ($\sqrt{58}$)
$ b.\qquad$ The distances are equal ($\sqrt{a^{2}+b^{2}}$)
Work Step by Step
a.
The distance from (7, 3) to the origin is
$\sqrt{(7-0)^{2}+(3-0)^{2}}=\sqrt{7^{2}+3^{2}}=\sqrt{49+9}=\sqrt{58}$.
The distance from (3, 7) to the origin is
$\sqrt{(3-0)^{2}+(7-0)^{2}}=\sqrt{3^{2}+7^{2}}=\sqrt{9+49}=\sqrt{58}$.
So, the points are the same distance from the origin.
b.
The distance from $(a, b)$ to the origin is
$\sqrt{(a-0)^{2}+(b-0)^{2}}=\sqrt{a^{2}+b^{2}}$.
The distance from $(b, a)$ to the origin is
$\sqrt{(b-0)^{2}+(a-0)^{2}}=\sqrt{b^{2}+a^{2}}=\sqrt{a^{2}+b^{2}}$.
So, the points are the same distance from the origin.
