# What is the length of the segment with endpoints (0,-1) and (4, 7)?

Length from (0,-1) to (4,7): $\textcolor{b l u e}{4 \sqrt{5}}$
The horizontal distance, $\Delta x$, between $\left(0 , - 1\right)$ and $\left(4 , 7\right)$ is $\left\mid 4 - 0 \right\mid = 4$
The vertical distance, $\Delta y$, between $\left(0 , - 1\right)$ and $\left(4 , 7\right)$ is $\left\mid 7 - \left(- 1\right) \right\mid = 8$
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{4}^{2} + {8}^{2}} = \sqrt{{4}^{2} \cdot \left(1 + {2}^{2}\right)} = 4 \sqrt{5}$