What is the distance between the points (0,0) and (3,4)?

What is the distance between the points (0,0) and (3,4)?

• A. 4
• B. 5
• C. 6
• D. 7

Answer: (B)

Distance between two points on a plane comes from the Pythagorean theorem. The horizontal change from (0,0) to (3,0) is 3 units, and the vertical change from (0,0) to (0,4) is 4 units. The straight-line distance is the hypotenuse of a right triangle with legs 3 and 4, so you use sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. So the distance between (0,0) and (3,4) is 5 units. This same idea underlies the general distance formula: you square the differences in coordinates, add them, and take the square root. If the coordinate differences were different, you’d get those other values, but for these points the result is 5.

Distance between two points on a plane comes from the Pythagorean theorem. The horizontal change from (0,0) to (3,0) is 3 units, and the vertical change from (0,0) to (0,4) is 4 units. The straight-line distance is the hypotenuse of a right triangle with legs 3 and 4, so you use sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. So the distance between (0,0) and (3,4) is 5 units. This same idea underlies the general distance formula: you square the differences in coordinates, add them, and take the square root. If the coordinate differences were different, you’d get those other values, but for these points the result is 5.