Subjects geometry

Distance Origin

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Distance Origin


1. The problem asks for the distance of the point $(5,4)$ from the origin $(0,0)$. 2. The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in the plane is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. Here, the origin is $(0,0)$ and the point is $(5,4)$, so: $$d = \sqrt{(5 - 0)^2 + (4 - 0)^2} = \sqrt{5^2 + 4^2}$$ 4. Calculate the squares: $$d = \sqrt{25 + 16} = \sqrt{41}$$ 5. Therefore, the distance of the point $(5,4)$ from the origin is: $$\boxed{\sqrt{41}}$$