Find the distance between the points $LaTeX: \displaystyle \left( 5, \ 17\right)$ and $LaTeX: \displaystyle \left( 12, \ 41\right)$ .

The distace formula gives $LaTeX: \displaystyle d=\sqrt{ ((12)-(5))^2 + ((41)-(17))^2 }=\sqrt{ 49 + 576 }$ . Simplifying gives $LaTeX: \displaystyle d = 25$ .