1. **Problem statement:** Find the length of line segment $PQ$ where $P(-1,1)$ and $Q(3,4)$. 2. **Formula used:** The distance 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. **Substitute values:** $$d = \sqrt{(3 - (-1))^2 + (4 - 1)^2} = \sqrt{(3 + 1)^2 + 3^2} = \sqrt{4^2 + 3^2}$$ 4. **Calculate:** $$d = \sqrt{16 + 9} = \sqrt{25} = 5$$ 5. **Answer:** The length of line $PQ$ is $5$ units.