Answer
$2\sqrt {37}$
Work Step by Step
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: $d=\sqrt {(2)^{2}+(-12)^{2}}=\sqrt {148}=2\sqrt {37}$