Final answer:
The distance between points u = (-3, 3) and v = (3, -3) is calculated using the distance formula. By substituting the coordinates into the formula and simplifying, the distance is found to be 6√2 units.
Step-by-step explanation:
The distance between points u = (-3, 3) and v = (3, -3) can be calculated using the distance formula, which is derived from the Pythagorean Theorem. The distance formula is √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
To find the distance between u and v, substitute the coordinates into the formula:
- Let x1 = -3 and y1 = 3 (point u).
- Let x2 = 3 and y2 = -3 (point v).
Then calculate the squares of the differences:
- (3 - (-3))^2 = (3 + 3)^2 = 36
- (-3 - 3)^2 = (-3 - 3)^2 = 36
Now, sum these values and take the square root:
√(36 + 36) = √72
Simplify the square root:
√72 = √(36 * 2) = 6√2
So, the distance between point u and point v is 6√2 units.