https://file.aiquickdraw.com/mathbot/file/1727245811870uc9b5i2s.jpg

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?

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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.

The sides of the square below are 8 units long. Each side of the square is parallel to an axis. What are the coordinates of point G on the square?

Discover how to find the coordinates of a square's vertex given a point and side length. This problem involves understanding properties of squares and coordinate geometry, perfect for students in Grades 6-8.

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