Given the line segment CD
Point M is the midpoint of CD
As shown:
[tex]\begin{gathered} C\colon(3a,2a) \\ D\colon(3,2) \\ M\colon(6,4) \end{gathered}[/tex]
The relation between the points is:
[tex]M=\frac{C+D}{2}[/tex]
Substitute with the points then solve for a:
[tex]\begin{gathered} (6,4)=\frac{(3a,2a)+(3,2)}{2} \\ 2\cdot(6,4)=(3a+3,2a+2) \\ (12,8)=(3a+3,2a+2) \\ So, \\ 3a+3=12 \\ 3a=12-3 \\ 3a=9 \\ a=\frac{9}{3}=3 \end{gathered}[/tex]
So, the answer will be: a = 3
