The coordinates of point F are (1, 9), with the midpoint M(5, 7) and point G(9, 5). The midpoint formula was used to determine F's coordinates from M and G.
The midpoint formula is given by:
![\[ M = \left( \frac{{x_1 + x_2}}{2}, \frac{{y_1 + y_2}}{2} \right) \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/uhui42ddjotpa9liii5iz552sxgw9houjb.png)
In this case, the midpoint M is given as
and point G is
. Let F have coordinates (x, y).
Using the midpoint formula:
![\[ 5 = \frac{{x + 9}}{2} \]\[ 7 = \frac{{y + 5}}{2} \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/7cowd85oege9u25xqs941pj9sogz88xpk2.png)
Solving these equations will give the coordinates of point F.
1. For the x-coordinate:
![\[ 5 = \frac{{x + 9}}{2} \]\[ 10 = x + 9 \]\[ x = 1 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/faqhbuj3w6ht81m326vt3w6xx4lpeu7pl8.png)
2. For the y-coordinate:
![\[ 7 = \frac{{y + 5}}{2} \]\[ 14 = y + 5 \]\[ y = 9 \]](https://img.qammunity.org/2022/formulas/mathematics/high-school/jp0pifrdsyisyhv7klijr43nebgzv0a2b3.png)
Therefore, the coordinates of point F are
.