The distance between two points A(x1,y1) and B(x2,y2) is given by:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In this problem we need to find the length of MB which is half AB, therefore the distance will be d/2 or:
[tex]\frac{d}{2}=\frac{\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}}{2}[/tex]Now, let's replace and solve
x1 = 4
y1 = -1
x2 = -2
y2 = 3
[tex]\begin{gathered} MB=\frac{d}{2}=\frac{\sqrt[]{(-2-4)^2+\mleft(3+1\mright)^2}}{2} \\ =\frac{1}{2}\cdot\sqrt[]{(-6)^2+(4)^2} \\ =\frac{1}{2}\sqrt[]{36+16} \\ =\frac{1}{2}\sqrt[]{52} \\ =\frac{1}{2}\cdot2\sqrt[]{13} \\ =\sqrt[]{13} \end{gathered}[/tex]Thus, the length of MB is SQRT(13) or approximately: 3.6
