Final answer:
The distance between the points E(7, -2) and F(-2, 10) is √177.
Step-by-step explanation:
To find the distance between the points E(7, -2) and F(-2, 10), we use the distance formula derived from the Pythagorean theorem. This formula is √[(x2 - x1)^2 + (y2 - y1)^2], where (x1, y1) and (x2, y2) are the coordinates of the two points.
Given the coordinates E(7, -2) and F(-2, 10), we can use the distance formula to find the distance between them:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates, we get:
d = √((-2 - 7)^2 + (10 - (-2))^2)
Simplifying, we have:
d = √(9^2 + 12^2) = √177
Therefore, the answer is ( √177 ), which corresponds to option A.