The distance between points (1,2) and (4,6) is?

• A. 3
• B. 4
• C. sqrt(50)
• D. 5

Answer: (D)

The distance between two coordinates comes from the Pythagorean theorem: the horizontal change and the vertical change form the legs of a right triangle, and the distance is the hypotenuse.

From (1,2) to (4,6), the horizontal difference is 4 − 1 = 3 and the vertical difference is 6 − 2 = 4. So the distance is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is the familiar 3-4-5 right triangle, so the distance is 5.