Find the distance between the points $LaTeX: \displaystyle \left( -14, \ 93\right)$ and $LaTeX: \displaystyle \left( 31, \ 121\right)$ .

The distace formula gives $LaTeX: \displaystyle d=\sqrt{ ((31)-(-14))^2 + ((121)-(93))^2 }=\sqrt{ 2025 + 784 }$ . Simplifying gives $LaTeX: \displaystyle d = 53$ .