Plot a rectangle on the coordinate plane where two vertices are located at (4, 2) and (4, 6). What are the coordinates of the remaining two vertices?

To determine the coordinates of the remaining two vertices of a rectangle when two vertices are given, we'll make some logical assumptions based on the properties of a rectangle. ### Given: - Two vertices of the rectangle are at **(4, 2)** and **(4, 6)**. ### Understanding the Rectangle: 1. **Vertical Side:** Since both given points share the same **x-coordinate (4)** but have different **y-coordinates**, these points form a **vertical side** of the rectangle. 2. **Rectangle Properties:** - Opposite sides of a rectangle are **equal in length** and **parallel**. - The other two vertices must also form a vertical side parallel to the one formed by the given points. ### Finding the Remaining Vertices: To complete the rectangle, we need two more points that: - Share the same **y-coordinates** as the given points (**2** and **6**), but have a **different x-coordinate**. - Ensure that the sides are **parallel** and **equal in length**. Let's denote the unknown x-coordinate as **"a"**. Therefore, the remaining two vertices will be: - **(a, 2)** - **(a, 6)** ### Example: If we choose **a = 8**, the remaining vertices would be: - **(8, 2)** - **(8, 6)** This choice results in a rectangle with sides: - **Vertical sides:** (4, 2) to (4, 6) and (8, 2) to (8, 6) - **Horizontal sides:** (4, 2) to (8, 2) and (4, 6) to (8, 6) ### Visualization: Here's how the rectangle would look with the additional vertices at **(8, 2)** and **(8, 6)**: ``` y | 6 | (4,6)________(8,6) | | | | | | 2 | (4,2)________(8,2) | +----------------------------- x 4 8 ``` ### General Solution: Without a specific value for **"a"**, the remaining two vertices can be expressed generally as: - **(a, 2)** - **(a, 6)** Where **a ≠ 4** to ensure that the points are distinct and form a valid rectangle. Feel free to choose any value for **a** based on the specific requirements or constraints of your problem!