1. You asked for points on the graph that are exactly five units away from the origin. 2. The distance from the origin to a point $(x,y)$ is given by the formula $$\sqrt{x^2 + y^2} = 5$$. 3. Squaring both sides, we get $$x^2 + y^2 = 25$$. 4. This is the equation of a circle centered at the origin with radius 5. 5. To find points on this circle, choose values for $x$ and solve for $y$: - If $x=0$, then $y=\pm 5$ giving points $(0,5)$ and $(0,-5)$. - If $x=3$, then $y=\pm \sqrt{25-9} = \pm 4$ giving points $(3,4)$ and $(3,-4)$. - If $x=4$, then $y=\pm \sqrt{25-16} = \pm 3$ giving points $(4,3)$ and $(4,-3)$. - If $x=5$, then $y=0$ giving point $(5,0)$. - If $x=-5$, then $y=0$ giving point $(-5,0)$. 6. These points are exactly five units from the origin on the graph.