https://file.aiquickdraw.com/mathbot/file/1725545548079301t6n6p.jpg

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.

What are the coordinates of the missing vertex?

Learn how to find the missing vertex of a square on a coordinate plane by using the properties of squares. This solution shows how to identify coordinates by analyzing parallel and perpendicular lines. Suitable for students in Grades 5-7.

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