We can calculate the magnitude of a vector as the distance between the initial and terminal points.
So if the initial and terminal points are (-5,8) and (2,3), we can calculate the magnitude as:
[tex]\begin{gathered} \mleft\Vert v\mleft\Vert=\sqrt[]{(y_2-y_1)^2+(x_2-x_1)^2}\mright?\mright? \\ \Vert v\Vert=\sqrt[]{(3-8)^2+(2-(-5)_{})^2} \\ \Vert v\Vert=\sqrt[]{(-5)^2+(7)^2} \\ \Vert v\Vert=\sqrt[]{25+49} \\ \Vert v\Vert=\sqrt[]{74} \\ \Vert v\Vert=8.60 \end{gathered}[/tex]
Answer: the magnitude is 8.60.
