## Precalculus (6th Edition) Blitzer

Yes, the line segment with endpoints $\left( -3,-3 \right)$ and $\left( 0,3 \right)$ has the same length as the line segment with endpoints $\left( 0,0 \right)$ and $\left( 3,6 \right)$ The length of the line segment with endpoints $\left( -3,-3 \right)$ and $\left( 0,3 \right)$ is given by \begin{align} & {{d}_{1}}=\sqrt{{{\left( 0-\left( -3 \right) \right)}^{2}}+{{\left( 3-\left( -3 \right) \right)}^{2}}} \\ & =\sqrt{{{\left( 3 \right)}^{2}}+{{\left( 6 \right)}^{2}}} \\ & =\sqrt{9+36} \\ & =\sqrt{45} \end{align}
The length of the line segment with endpoints $\left( 0,0 \right)$ and $\left( 3,6 \right)$ is given by \begin{align} & {{d}_{2}}=\sqrt{{{\left( 3-\left( 0 \right) \right)}^{2}}+{{\left( 6-\left( 0 \right) \right)}^{2}}} \\ & =\sqrt{{{\left( 3 \right)}^{2}}+{{\left( 6 \right)}^{2}}} \\ & =\sqrt{36+9} \\ & =\sqrt{45} \end{align} After application of the distance formula, the lengths of the provided two line segments are the same.