Which of the following are the coordinates of a rectangle with a length of 8 units and width of 5 units in the coordinate plane? \( (2,4),(-6,4),(2,0),(-6,0) \) \( (5,0),(-2,0),(5,5),(-2,5) \) \( (4,1),(-4,1),(4,6),(-4,6) \) \( (3,7),(-3,7),(3,1),(-3,1) \)

To determine which set of coordinates represents a rectangle with a length of 8 units and a width of 5 units, we need to check the distances between the points in each set. 1. **Set 1: \( (2,4),(-6,4),(2,0),(-6,0) \)** - Length (horizontal distance between \( (2,4) \) and \( (-6,4) \)): \[ |2 - (-6)| = |2 + 6| = 8 \text{ units} \] - Width (vertical distance between \( (2,4) \) and \( (2,0) \)): \[ |4 - 0| = 4 \text{ units} \] - This set does not match the required dimensions. 2. **Set 2: \( (5,0),(-2,0),(5,5),(-2,5) \)** - Length (horizontal distance between \( (5,0) \) and \( (-2,0) \)): \[ |5 - (-2)| = |5 + 2| = 7 \text{ units} \] - Width (vertical distance between \( (5,0) \) and \( (5,5) \)): \[ |0 - 5| = 5 \text{ units} \] - This set does not match the required dimensions. 3. **Set 3: \( (4,1),(-4,1),(4,6),(-4,6) \)** - Length (horizontal distance between \( (4,1) \) and \( (-4,1) \)): \[ |4 - (-4)| = |4 + 4| = 8 \text{ units} \] - Width (vertical distance between \( (4,1) \) and \( (4,6) \)): \[ |1 - 6| = 5 \text{ units} \] - This set matches the required dimensions. 4. **Set 4: \( (3,7),(-3,7),(3,1),(-3,1) \)** - Length (horizontal distance between \( (3,7) \) and \( (-3,7) \)): \[ |3 - (-3)| = |3 + 3| = 6 \text{ units} \] - Width (vertical distance between \( (3,7) \) and \( (3,1) \)): \[ |7 - 1| = 6 \text{ units} \] - This set does not match the required dimensions. Based on the calculations, the only set of coordinates that represents a rectangle with a length of 8 units and a width of 5 units is: **Set 3: \( (4,1),(-4,1),(4,6),(-4,6) \)**.