Final answer:
The distance between points u = (-3, 3) and v = (3, -3) is found using the distance formula, resulting in the square root of 72, or approximately 8.49 units.
Step-by-step explanation:
To find the distance between two points (u and v) in a plane, you can use the distance formula, which is derived from the Pythagorean theorem. The formula is: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
In this case, for point u = (-3, 3) and point v = (3, -3), plug the coordinates into the formula as follows: distance = sqrt((3 - (-3))^2 + (-3 - 3)^2), which simplifies to distance = sqrt((6)^2 + (-6)^2) = sqrt(36 + 36) = sqrt(72). The exact distance between the points u and v is then the square root of 72, which can be simplified to 6 times the square root of 2, or approximately 8.49 units.