Given:
A line segment with a midpoint = (4, 4)
The segment has the endpoints (1,2) and (a,b)
We will find the point (a, b) using the following formula:
[tex]M=\frac{P+Q}{2}[/tex]Where M is the midpoint of the line segment PQ
So, we can write the following equation:
[tex](4,4)=\frac{(1,2)+(a,b)}{2}[/tex]Solve for (a, b) as follows:
[tex]\begin{gathered} 2*(4,4)=(1,2)+(a,b) \\ (8,8)=(1+a,2+b) \\ \\ 1+a=8\to a=8-1=7 \\ 2+b=8\to b=8-2=6 \\ \\ (a,b)=(7,6) \end{gathered}[/tex]So, the answer will be (a,b) = (7,6)
