Answer:
[tex]\large\boxed{|\overrightarrow{CD}|=3\sqrt{61}}[/tex]
Step-by-step explanation:
The formula of a magnitude of vector:
[tex]|\overrightarrow{AB}|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where
[tex]A(x_1,\ y_1),\ B(x_2,\ y_2)[/tex]
We have:
[tex]C(10,\ 10),\ D(-8,\ -5)[/tex]
Substitute:
[tex]|\overrightarrow{CD}|=\sqrt{(-8-10)^2+(-5-10)^2}\\\\|\overrightarrow{CD}|=\sqrt{(-18)^2+(-15)^2}\\\\|\overrightarrow{CD}|=\sqrt{324+225}\\\\|\overrightarrow{CD}|=\sqrt{549}\\\\|\overrightarrow{CD}|=\sqrt{(9)(61)}\\\\|\overrightarrow{CD}|=\sqrt{9}\cdot\sqrt{61}\\\\|\overrightarrow{CD}|=3\sqrt{61}[/tex]
