What is the distance between the points (1, 4) and (4, 8)?

Question

Accepted Answer

5. The correct answer is 5. Using the distance formula: d = √[(4-1)² + (8-4)²] = √[9 + 16] = √25 = 5. This is also a 3-4-5 right triangle, one of the most common Pythagorean triples.

The value 7 adds the differences (3 + 4 = 7) instead of using the Pythagorean theorem. This confuses Manhattan distance (sum of absolute differences) with Euclidean distance. The value 25 is d², not d; it results from forgetting to take the square root in the distance formula. The value √7 likely comes from a computational error in squaring the differences or from adding incorrectly.

The distance formula d = √[(x₂-x₁)² + (y₂-y₁)²] is derived from the Pythagorean theorem and is used extensively in analytic geometry on the CLEP exam. Related formulas include the midpoint formula ((x₁+x₂)/2, (y₁+y₂)/2). Students should recognize common Pythagorean triples (3-4-5, 5-12-13, 8-15-17) to speed up calculations.

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