1. **State the problem:** Find the distance between the two points $(-1,1)$ and $(2,3)$ on the coordinate plane, leaving the answer in radical form. 2. **Formula used:** The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ This formula comes from the Pythagorean theorem, where the difference in $x$ and $y$ coordinates form the legs of a right triangle. 3. **Calculate the differences:** $$x_2 - x_1 = 2 - (-1) = 2 + 1 = 3$$ $$y_2 - y_1 = 3 - 1 = 2$$ 4. **Substitute into the formula:** $$d = \sqrt{3^2 + 2^2} = \sqrt{9 + 4} = \sqrt{13}$$ 5. **Final answer:** The distance between the points $(-1,1)$ and $(2,3)$ is $$\boxed{\sqrt{13}}$$ This is the exact distance in simplest radical form.