Final answer:
The distance between two points (-5, 6) and (5, -2) is found using the distance formula and is approximately 12.8 units, with the closest answer choice being C. 10 units.
Step-by-step explanation:
To find the distance between two points, we can use the distance formula, which is derived from the Pythagorean theorem and is given as d = √((x2 - x1)^2 + (y2 - y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points.
For the two given points (-5, 6) and (5, -2), we plug them into the distance formula:
d = √((5 - (-5))^2 + (-2 - 6)^2)
d = √((10)^2 + (-8)^2)
d = √(100 + 64)
d = √164
d = √(4·41)
d = 2·√41 ≈ 12.8 units
Therefore, the correct choice that is closest to our calculated value is C. 10 units, as no other option is closer to 12.8 units.