APPENDIX B - Coordinate Geometry and Lines - B Exercises - Page A 15: 5

$2\sqrt {37}$

To find the distance between $(2,5)$ and $(4,-7)$, 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: $d=\sqrt {(4-2)^{2}+(-7-5)^{2}}$. We then simplify to arrive at the answer: $d=\sqrt {2^{2}+12^{2}}=\sqrt {148} = 2\sqrt {37}$.