I see you've uploaded an image with a grid showing three vertices of a square and a question asking for the coordinates of the missing fourth vertex.

From the grid in the image, it appears that the known vertices of the square are approximately located at:

• (1, 1)
• (1, 5)
• (5, 5)

We need to determine the fourth vertex. Since it is a square, the sides are equal, and the vertices should form right angles.

Looking at the points, two of the given vertices are vertically aligned (along the same x-coordinate), and one vertex forms a horizontal line with another (along the same y-coordinate). The missing vertex must complete the square.

The x-coordinate of the missing point must be 5 (since two points share an x-coordinate of 1) and the y-coordinate must be 1 (since two points share a y-coordinate of 5).

Therefore, the coordinates of the missing vertex are:

• (5, 1)

Would you like further details or have any questions about how this solution was found?

Here are 5 related questions to expand on this:

1. How can you determine the slope of a line between two points?
2. What are the properties of a square in terms of side lengths and angles?
3. How can you calculate the distance between two points in a coordinate plane?
4. What is the formula for the area of a square, and how would you apply it to these vertices?
5. How would this problem change if it were a rectangle instead of a square?

Tip: When working with geometric shapes on a coordinate plane, always look for parallel or perpendicular lines, which can help determine missing points or verify shape properties.