Given that $x + y = 13$ and $xy = 24$, find the distance from the point $(x, y)$ to the origin.
The magnitude of $(x, y)$ is $\sqrt{x^2 + y^2}$. To find $x^2 + y^2$, I can use the given equations $x + y = 13$ and $xy = 24$. If I square both sides of $x + y = 13$, I get $x^2 + 2xy + y^2 = 169$. I can subtract $2xy$ from both sides, and since $xy = 24$, I get $x^2 + y^2 = 169 - 2 \cdot 24 = 121$. Now I can plug this into the formula for the magnitude, and I get $\sqrt{x^2 + y^2} = \sqrt{121} = 11$. This is the distance from $(x, y)$ to the origin.

