The coordinates of point E are (18 , 21).
As F is the midpoint of line EFG, we can use the midpoint formula to solve for the coordinates of E.
Given:
Point F has coordinates (11, 24).
Point G has coordinates (4, 27).
The midpoint formula states that the midpoint F between points E and G is:
![\[F = \left((x_E + x_G)/(2), (y_E + y_G)/(2)\right)\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/zi7aeqng6idyz44ecekbgom81nxfkubhnf.png)
And we're given that F is (11, 24).
Now, substituting the coordinates of F and G:
![\[(x_E + 4)/(2) = 11 \implies x_E + 4 = 22 \implies x_E = 22 - 4 = 18\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/wbv8wko4pupa5lwjx89js6iadgdq6xuktn.png)
![\[(y_E + 27)/(2) = 24 \implies y_E + 27 = 48 \implies y_E = 48 - 27 = 21\]](https://img.qammunity.org/2024/formulas/mathematics/high-school/1f118xtxaxf8z1rclmvvkonh4hzxhje22v.png)
Therefore, using the midpoint formula and the given information, the coordinates of point E are (18, 21), confirming the solution provided earlier.