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

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

• A. 3
• B. 4
• C. sqrt(20)
• D. 5

Answer: (D)

The distance between two points on a plane comes from the Pythagorean theorem: the straight-line distance is the hypotenuse of a right triangle built from how far apart the points are horizontally and vertically. From (1, 2) to (4, 6), the horizontal change is 3 (4 − 1) and the vertical change is 4 (6 − 2). So the distance is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is a classic 3-4-5 triangle, a reliable reminder that you must combine both differences to get the true distance.

The distance between two points on a plane comes from the Pythagorean theorem: the straight-line distance is the hypotenuse of a right triangle built from how far apart the points are horizontally and vertically. From (1, 2) to (4, 6), the horizontal change is 3 (4 − 1) and the vertical change is 4 (6 − 2). So the distance is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is a classic 3-4-5 triangle, a reliable reminder that you must combine both differences to get the true distance.