The distance between (0,0) and (3,4) is?

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Multiple Choice

The distance between (0,0) and (3,4) is?

Explanation:
The distance between two points on a plane uses the distance formula: distance = sqrt((x2 − x1)² + (y2 − y1)²). For (0,0) and (3,4), the differences are 3 and 4. Squaring gives 9 and 16, and adding them yields 25, whose square root is 5. So the distance is 5—the familiar 3-4-5 right triangle. The other numbers don’t match this distance: 3 would imply moving only along one axis, √41 would come from differences like 5 and 4 (since 5² + 4² = 41), and 8 isn’t the result of these coordinate changes. The key idea is recognizing the Pythagorean relationship between the coordinate differences.

The distance between two points on a plane uses the distance formula: distance = sqrt((x2 − x1)² + (y2 − y1)²). For (0,0) and (3,4), the differences are 3 and 4. Squaring gives 9 and 16, and adding them yields 25, whose square root is 5. So the distance is 5—the familiar 3-4-5 right triangle.

The other numbers don’t match this distance: 3 would imply moving only along one axis, √41 would come from differences like 5 and 4 (since 5² + 4² = 41), and 8 isn’t the result of these coordinate changes. The key idea is recognizing the Pythagorean relationship between the coordinate differences.

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