Final answer:
The coordinates exactly 5 units from (2, -1) are (5, 3), (-2, 2), and (-3, -1), as determined by applying the distance formula to each set of points.
Step-by-step explanation:
To determine which coordinates are exactly 5 units away from the point (2, -1), we can use the distance formula between two points in a Cartesian coordinate system, which is √((x2 - x1)² + (y2 - y1)²). We will apply this formula to each of the provided coordinates to check if the distance between them and (2, -1) is 5.
For the point (3, 4), the distance is √((3 - 2)² + (4 - (-1))²) = √(1 + 25) = √26, which is not 5.
For the point (5, 3), the distance is √((5 - 2)² + (3 - (-1))²) = √(9 + 16) = 5.
For the point (-2, 2), the distance is √((-2 - 2)² + (2 - (-1))²) = √(16 + 9) = 5.
For the point (-3, -1), the distance is √((-3 - 2)² + (-1 - (-1))²) = √(25 + 0) = 5.
Therefore, the coordinates that are exactly 5 units from (2, -1) are (5, 3), (-2, 2), and (-3, -1).