To find the coordinates of the vertices of a rectangle that is 6 units long and 4 units wide, with one vertex at the origin and the longer side lying on the x-axis in the first quadrant, we can follow these steps:
### Step-by-Step Solution:
1. **Identify the Position of the Rectangle**:
- Since one vertex is at the origin (0, 0) and the longer side (length 6) lies on the x-axis, we can place the rectangle in the first quadrant.
2. **Determine the Coordinates of the Vertices**:
- The rectangle's longer side is along the x-axis, which means it will extend horizontally from the origin.
- The coordinates of the vertex at the origin are (0, 0).
3. **Calculate the Coordinates of the Other Vertices**:
- The rectangle is 6 units long, so the vertex on the x-axis opposite to the origin will be at (6, 0).
- The width of the rectangle is 4 units, which means the height will extend vertically from the x-axis.
- The vertex directly above the origin (0, 0) will be at (0, 4).
- The vertex directly above the point (6, 0) will be at (6, 4).
4. **List All the Coordinates**:
- The coordinates of the vertices of the rectangle are:
- Vertex A: (0, 0)
- Vertex B: (6, 0)
- Vertex C: (6, 4)
- Vertex D: (0, 4)
### Final Answer:
The coordinates of the vertices of the rectangle are:
- A (0, 0)
- B (6, 0)
- C (6, 4)
- D (0, 4)
