Which of the following points is farthest from the origin: $(0,5)$, $(1,2)$, $(3,-4)$, $(6,0)$, $(-1,-2)?$
I want to find the distance of each point from the origin, which is the point $(0,0)$. The distance formula says that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. So, for each point, I can plug in the coordinates and simplify the expression. For $(0,5)$, the distance is $\sqrt{(0-0)^2+(5-0)^2}=\sqrt{0+25}=\sqrt{25}=5$. For $(1,2)$, the distance is $\sqrt{(1-0)^2+(2-0)^2}=\sqrt{1+4}=\sqrt{5}$. For $(3,-4)$, the distance is $\sqrt{(3-0)^2+(-4-0)^2}=\sqrt{9+16}=\sqrt{25}=5$. For $(6,0)$, the distance is $\sqrt{(6-0)^2+(0-0)^2}=\sqrt{36+0}=\sqrt{36}=6$. For $(-1,-2)$, the distance is $\sqrt{(-1-0)^2+(-2-0)^2}=\sqrt{1+4}=\sqrt{5}$. Comparing these distances, I see that the largest one is $6$, which corresponds to the point $(6,0)$. Therefore, the point that is farthest from the origin is $(6,0)$. 