Question

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

Answer 1

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