# APPENDIX B - Coordinate Geometry and Lines - B Exercises: 1

$5$

#### Work Step by Step

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: $d=\sqrt {3^{2}+4^{2}}=\sqrt {25} = 5$.

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