What is the distance between the points (1, 2) and (4, 6) on a coordinate plane?

What is the distance between the points (1, 2) and (4, 6) on a coordinate plane?

• A. 4
• B. 6
• C. 5
• D. 7

Answer: (C)

The distance between two points on a coordinate plane comes from the Pythagorean theorem: the horizontal change and the vertical change between the points form the legs of a right triangle, and the distance is the hypotenuse. From (1, 2) to (4, 6), the horizontal change is 4 − 1 = 3 and the vertical change is 6 − 2 = 4. Squaring and adding gives 3^2 + 4^2 = 9 + 16 = 25. The square root of 25 is 5, so the distance is 5 units.

The distance between two points on a coordinate plane comes from the Pythagorean theorem: the horizontal change and the vertical change between the points form the legs of a right triangle, and the distance is the hypotenuse. From (1, 2) to (4, 6), the horizontal change is 4 − 1 = 3 and the vertical change is 6 − 2 = 4. Squaring and adding gives 3^2 + 4^2 = 9 + 16 = 25. The square root of 25 is 5, so the distance is 5 units.