Answer
$a)$ Points $(7,3)$ and $(3,7)$ are the same distance from the origin.
$b)$ Points $(a,b)$ and $(b,a)$ are the same distance from the origin.
Work Step by Step
Use the formula for the distance between two points to do this problem. The formula is $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
$a)$ $(7,3)$ $;$ $(3,7)$
Find the distance between point $(7,3)$ and the origin:
$d_{1}=\sqrt{(7-0)^{2}+(3-0)^{2}}=\sqrt{49+9}=\sqrt{50}=5\sqrt{2}$
Find the distance between point $(3,7)$ and the origin:
$d_{2}=\sqrt{(3-0)^{2}+(7-0)^{2}}=\sqrt{9+49}=\sqrt{50}=5\sqrt{2}$
Since $d_{1}=d_{2}$, points $(7,3)$ and $(3,7)$ are the same distance from the origin.
$b)$ $(a,b)$ $;$ $(b,a)$
Find the distance between point $(a,b)$ and the origin:
$d_{1}=\sqrt{(a-0)^{2}+(b-0)^{2}}=\sqrt{a^{2}+b^{2}}$
Find the distance between point $(b,a)$ and the origin:
$d_{2}=\sqrt{(b-0)^{2}+(a-0)^{2}}=\sqrt{b^{2}+a^{2}}=\sqrt{a^{2}+b^{2}}$
Since $d_{1}=d_{2}$, points $(a,b)$ and $(b,a)$ are the same distance from the origin.