What is the distance between the points (2, -1) and (5, 3)?

What is the distance between the points (2, -1) and (5, 3)?

• A. 5
• B. sqrt(34)
• C. 4
• D. sqrt(20)

Answer: (A)

Distance in the plane between two points is found using the distance formula, which comes from the Pythagorean theorem. Look at how much you move horizontally and vertically from one point to the other: the horizontal change is 5 − 2 = 3, and the vertical change is 3 − (−1) = 4. Square both changes and add them: 3^2 + 4^2 = 9 + 16 = 25. The distance is the square root of that sum, which is √25 = 5. So the distance is 5. If you tried other options, they would come from different sums of squares (for example, 34 or 20), which don’t match these horizontal and vertical differences.

Distance in the plane between two points is found using the distance formula, which comes from the Pythagorean theorem. Look at how much you move horizontally and vertically from one point to the other: the horizontal change is 5 − 2 = 3, and the vertical change is 3 − (−1) = 4. Square both changes and add them: 3^2 + 4^2 = 9 + 16 = 25. The distance is the square root of that sum, which is √25 = 5. So the distance is 5. If you tried other options, they would come from different sums of squares (for example, 34 or 20), which don’t match these horizontal and vertical differences.