Write the coordinates os the fourth vertex of a square when three of its vertices are given by (1,2) (5,2) (5, -2).

Answer

To find the coordinates of the fourth vertex of a square when three vertices are given, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Vertices**:
We have three vertices of the square:
- A(1, 2)
- B(5, 2)
- C(5, -2)

2. **Plot the Points**:
We can visualize the points on a Cartesian plane.
- Point A is at (1, 2)
- Point B is at (5, 2)
- Point C is at (5, -2)

3. **Determine the Length of the Sides**:
The distance between points A and B is the length of one side of the square.
- The distance AB = x2 - x1 = 5 - 1 = 4 units (horizontal distance).
- The distance BC = y2 - y1 = 2 - (-2) = 4 units (vertical distance).

4. **Identify the Fourth Vertex**:
Since we have two points on the same horizontal line (A and B) and one point (C) directly below B, we can find the fourth vertex (D) by moving vertically down from A or horizontally left from C.
- The fourth vertex D will be at the same x-coordinate as A and the same y-coordinate as C.
- Therefore, D = (1, -2).

5. **Conclusion**:
The coordinates of the fourth vertex of the square are (1, -2).

### Final Answer:
The coordinates of the fourth vertex are **(1, -2)**.

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