To determine the distance between two points on the coordinate system you can use the following formula, which is derived from the Pythagorean theorem:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)}[/tex]
Where
(x₁,y₁) are the coordinates of one of the endpoints of the line
(x₂,y₂) are the coordinates of the second endpoint of the line
Using C(8,-3) as (x₂,y₂) and D(-9,-6) as (x₁,y₁), you can calculate the length of CD as follows:
[tex]\begin{gathered} d_{CD}=\sqrt[]{(8-(-9))^2+((-3)-(-6))^2} \\ d_{CD}=\sqrt[]{(8+9)^2+((-3)+6)^2} \\ d_{CD}=\sqrt[]{17^2+3^2} \\ d_{CD}=\sqrt[]{289+9} \\ d_{CD}=\sqrt[]{298} \\ d_{CD}=17,26\approx17.3 \end{gathered}[/tex]
The length of CD rounded to the nearest tenth is 17.3 units
