What is the distance between (0, 0) and (3, 4) in the Cartesian plane?

What is the distance between (0, 0) and (3, 4) in the Cartesian plane?

• A. 5
• B. 6
• C. 7
• D. 8

Answer: (A)

Think of the segment from the origin to (3, 4) as the hypotenuse of a right triangle whose legs are the horizontal and vertical differences, 3 and 4. Using the Pythagorean theorem, the distance is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is the familiar 3-4-5 triangle, so the distance between the points is 5. The other distances (6, 7, 8) would require different leg lengths, not the 3 and 4 we have here.

Think of the segment from the origin to (3, 4) as the hypotenuse of a right triangle whose legs are the horizontal and vertical differences, 3 and 4. Using the Pythagorean theorem, the distance is sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is the familiar 3-4-5 triangle, so the distance between the points is 5. The other distances (6, 7, 8) would require different leg lengths, not the 3 and 4 we have here.