Appendix B - Coordinate Geometry and Lines - B Exercises - Page A15: 1

$5$

To find the distance between $(1,1)$ and $(4,5)$, we use the distance formula: $d=\sqrt {(x_{2}−x_{1})^{2}+(y_{2}−y_{1})^{2}}$. We plug in the given x and y values: $d=\sqrt {(4−1)^{2}+(5−1)^{2}}$. We then simplify to arrive at the answer: $d=\sqrt {3^{2}+4^{2}}=\sqrt {25}=5$