Geometry and TrigonometryMediumDistance in the coordinate plane
Geometry and Trigonometry practice question
What is the distance between the points (1, 2) and (4, 6) in the coordinate plane?
- A. 5Correct
- B. 7
- C. √7
- D. 25
Answer: A. 5
Distance = √[(4 − 1)² + (6 − 2)²] = √[9 + 16] = √25 = 5. This is a 3-4-5 right triangle laid on the grid.
Why the other answers are wrong
- B. 7
- You added the leg lengths (3 + 4) instead of using the Pythagorean theorem; √(3² + 4²) = 5.
- C. √7
- You added the differences before squaring: √(3 + 4). The formula squares each difference first: √(9 + 16) = √25 = 5.
- D. 25
- 25 is the value under the radical — you stopped one step early. Take the square root: √25 = 5.
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