jmc

We find the distance for all the points using the distance formula: For $(1,4)$: $\sqrt{(1-0{)}^2+(4-0{)}^2}=\sqrt{17}$ For $(3,5)$: $\sqrt{(3-0{)}^2+(5-0{)}^2}=\sqrt{34}$ For $(-6,0)$: $\sqrt{(-6-0{)}^2+(0-0{)}^2}=\sqrt{36}$ For $(-4,-2)$: $\sqrt{(-4-0{)}^2+(-2-0{)}^2}=\sqrt{20}$ Therefore, the point farthest from the origin is $\boxed{(-6,0)}$.