Appendix B - Coordinate Geometry and Lines - B Exercises - Page A15: 2

$2\sqrt {29}$

To find the distance between $(1,-3)$ and $(5,7)$, 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: $d=\sqrt {(5−1)^{2}+(7−(-3))^{2}}$. We then simplify to arrive at the answer: $d=\sqrt {4^{2}+10^{2}}=\sqrt {116}=2\sqrt {29}$