Answer:
Other point F ( 6 ,14).
Step-by-step explanation:
Given : The midpoint of EF is M(4, 10). One endpoint is E(2, 6).
To find : Find the coordinates of the other endpoint F.
Solution : We have given that
Line EF have mid point M ( 4 ,10)
One end point E ( 2 ,6) .
Let other point F ( [tex]x_{2} ,y_{2}[/tex])
Mid point segment formula ( M) : [tex](\frac{x_{1}+x_{2}}{2} , \frac{y_{1}+y_{2}}{2})[/tex].
[tex]\frac{x_{1}+x_{2}}{2}[/tex] = 4
Plug [tex]x_{1}[/tex] = 2.
[tex]\frac{2+x_{2}}{2}[/tex] = 4
On multiplying both side by 2
2 + [tex]x_{2}[/tex] = 8
[tex]x_{2}[/tex] = 8- 2
[tex]x_{2}[/tex] = 6.
[tex]\frac{y_{1}+y_{2}}{2}[/tex] = 10.
Plug [tex]y_{1}[/tex] = 6.
[tex]\frac{6+y_{2}}{2}[/tex] = 10.
On multiplying both side by 2
6 +[tex]y_{2}[/tex] = 20
[tex]y_{2}[/tex] = 20 - 6
[tex]y_{2}[/tex] = 14.
Therefore, Other point F ( 6 ,14).
