Compute the distance between (1,2) and (4,6). Which value is correct?

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Multiple Choice

Compute the distance between (1,2) and (4,6). Which value is correct?

Explanation:
The distance between two points uses the Pythagorean idea: distance = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. For (1, 2) and (4, 6), the horizontal change is 4 − 1 = 3 and the vertical change is 6 − 2 = 4. So distance = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is the familiar 3-4-5 right-triangle result. The other values would require a larger sum of squares than 25, so they don't fit.

The distance between two points uses the Pythagorean idea: distance = sqrt[(x2 − x1)^2 + (y2 − y1)^2]. For (1, 2) and (4, 6), the horizontal change is 4 − 1 = 3 and the vertical change is 6 − 2 = 4. So distance = sqrt(3^2 + 4^2) = sqrt(9 + 16) = sqrt(25) = 5. This is the familiar 3-4-5 right-triangle result. The other values would require a larger sum of squares than 25, so they don't fit.

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