From the image provided, we see that a square is drawn on the coordinate plane, with side lengths of 8 units. The coordinates of point $E$ are given as $(1, 5)$, and the square's sides are parallel to the axes.

We are tasked with finding the coordinates of point $G$, which lies diagonally opposite to point $E$.

Step-by-step reasoning:

• Since the square's sides are parallel to the axes, we can infer that the change in the x and y coordinates between diagonally opposite vertices must both be 8 units.
• $E(1, 5)$ is one corner of the square. To find the coordinates of the diagonally opposite point $G$, we add 8 to the x-coordinate and subtract 8 from the y-coordinate of $E$:
  • The x-coordinate of $G$: $1 + 8 = 9$
  • The y-coordinate of $G$: $5 - 8 = -3$

Thus, the coordinates of point $G$ are $(9, -3)$.

Would you like further clarification on any part of this solution?

Here are 5 related questions to deepen your understanding:

1. What are the coordinates of point $H$, which is next to $G$ on the x-axis?
2. Can you find the coordinates of point $F$, opposite to $H$?
3. How would the solution change if the square's side length were different?
4. How can you determine the center of the square using the coordinates of $E$ and $G$?
5. What would the coordinates be if the square were rotated 45 degrees about its center?

Tip: For shapes on coordinate planes, using symmetry and the relationship between vertices can simplify finding coordinates of other points.