91Ó°ÊÓ

Coordinates are given as$\left(−6,7\right)$ and$\left(0,0\right)$

The distance (d) between the points$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ is given by:

$d=\sqrt{{\left(x_2−x_1\right)}^2+{\left(y_2−y_1\right)}^2}$

Therefore, the distance (d) between the points$\left(−6,7\right)$ and$\left(0,0\right)$ is:

role="math" localid="1648014039812" $$\begin{gathered} d=\sqrt{{\left(0−\left(−6\right)\right)}^2+{\left(0−7\right)}^2} \\ =\sqrt{{\left(0+6\right)}^2+{\left(−7\right)}^2} \\ =\sqrt{6^2+7^2} \\ =\sqrt{36+49} \\ =\sqrt{85} \\ =9.2195445 \\ ≈9.22\left(\text{roundedtothenearesthundredth}\right) \end{gathered}$$

Therefore, the distance (d) between the points$\left(−6,7\right)$ and$\left(0,0\right)$ is 9.22.

The midpoint formula states that the midpoint M of a line segment with endpoints at$\left(x_1,y_1\right)$ and$\left(x_2,y_2\right)$ is given by $M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$.

The midpoint (M) of the line segment with endpoints at$\left(−6,7\right)$ and$\left(0,0\right)$ is given by:

$$\begin{gathered} M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right) \\ =\left(\frac{−6+0}{2},\frac{7+0}{2}\right) \\ =\left(\frac{−6}{2},\frac{7}{2}\right) \\ =\left(−3,3.5\right) \end{gathered}$$

Therefore, the midpoint of the line segment with the endpoints at$\left(−6,7\right)$ and$\left(0,0\right)$ is role="math" localid="1648014451216" $\left(−3,3.5\right)$.