ANSWER
[tex]r = 5 \sqrt{5 } [/tex]
EXPLANATION
Given that (x,y)=(5,10), we want to find r.
We use the relation:
[tex]r = \sqrt{ {x}^{2} + {y}^{2} } [/tex]
We substitute x=5 and y=10 into the formula to get,
[tex]r = \sqrt{ {5}^{2} + {10}^{2} } [/tex]
This implies that,
[tex]r = \sqrt{ 25+ 100 } [/tex]
[tex]r = \sqrt{125} [/tex]
[tex]r = 5 \sqrt{5 } [/tex]
