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Point M is the midpoint of CD. What us the value of a in the figure?

Point M is the midpoint of CD. What us the value of a in the figure?-example-1
User RodSarhan
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Given the line segment CD

Point M is the midpoint of CD

As shown:


\begin{gathered} C\colon(3a,2a) \\ D\colon(3,2) \\ M\colon(6,4) \end{gathered}

The relation between the points is:


M=(C+D)/(2)

Substitute with the points then solve for a:


\begin{gathered} (6,4)=((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=(9)/(3)=3 \end{gathered}

So, the answer will be: a = 3

User Aerilys
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