Final answer:
The distance between the points (3, -4) and (5, 6) is found by using the distance formula and is approximately 10 units, which corresponds to answer choice A.
Step-by-step explanation:
The distance between two points (x1, y1) and (x2, y2) in a Cartesian plane is calculated using the distance formula: \( \sqrt{(x2 - x1)^2 + (y2 - y1)^2} \). Applying this formula to the points (3, -4) and (5, 6), we find:
Distance = \( \sqrt{(5 - 3)^2 + (6 - (-4))^2} \)
= \( \sqrt{2^2 + 10^2} \)
= \( \sqrt{4 + 100} \)
= \( \sqrt{104} \)
= 10.2 (approx.)
Therefore, the correct answer is A) 10 units.