Answer :
[tex]coordinates\ of\ Q(x,y)\\\\
P(5,2)=(\frac{2+x}{2}\ ;\ \frac{0+y}{2})\\\\5=\frac{2+x}{2}\ \ |*2\\\\10=2+x\\\\
10-2=x\\\\x=8\\\\
2=\frac{0+y}{2}\ \ |*2\\\\
4=y\\\\
Q=(8,4)[/tex]
[tex]N(2,0),\ \ Q(x,y) \ \ midpoint : P(5,2)\\\\ Given \ the \ two \ points \ (x _{1}, y _{1}) and (x _{2}, y _{2}), \\the \ midpoint \ is \ given \ by \ the \ formula: \\\\ (x,y)=(\frac{x_{1}+x_{2}}{2};\frac{y_{1}+y_{2}}{2})\\\\(5,2)=(\frac{2+ x}{2};\frac{0+y}{2}) \frac{2+ x}{2}=5 \ \[/tex]
[tex]\frac{2+ x}{2}=5 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\2+x=10\ \ |\ subtract\ 2 \ to\ both\ sides \\\\x=8[/tex]
[tex]\frac{0+y}{2}=2 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\y=4 \\\\Answer: \ Q (8,4)[/tex]
[tex]\frac{2+ x}{2}=5 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\2+x=10\ \ |\ subtract\ 2 \ to\ both\ sides \\\\x=8[/tex]
[tex]\frac{0+y}{2}=2 \ \ |\ multiply\ both\ sides\ by\ 2 \\\\y=4 \\\\Answer: \ Q (8,4)[/tex]
