1. **State the problem:** Find the distance between the points $(1,2)$ and $(4,6)$ using the Pythagorean theorem. 2. **Formula:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. **Calculate the differences:** $$x_2 - x_1 = 4 - 1 = 3$$ $$y_2 - y_1 = 6 - 2 = 4$$ 4. **Apply the formula:** $$d = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25}$$ 5. **Simplify:** $$d = 5$$ 6. **Points to graph:** The points to plot are $(1,2)$ and $(4,6)$. This will help you visualize the distance between them on a coordinate plane.