What is the distance between the points (2, 3) and (5, 11) in the coordinate plane?

• A. 8
• B. sqrt(65)
• C. sqrt(72)
• D. sqrt(73)

Answer: (D)

To find the distance between two points on a coordinate plane, use the Pythagorean theorem. The horizontal difference between the points is 5 − 2 = 3, and the vertical difference is 11 − 3 = 8. These form the legs of a right triangle, and the distance between the points is the hypotenuse: sqrt(3^2 + 8^2) = sqrt(9 + 64) = sqrt(73). So the distance is sqrt(73).