The distance between points (1, 4) and (4, -2) is which of the following expressions?

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Multiple Choice

The distance between points (1, 4) and (4, -2) is which of the following expressions?

Explanation:
You use the distance formula to find how far apart two points are. For points (x1, y1) = (1, 4) and (x2, y2) = (4, -2), the distance is sqrt[(x2 − x1)^2 + (y2 − y1)^2]. Compute the differences: x2 − x1 = 4 − 1 = 3, y2 − y1 = −2 − 4 = −6. Square them: 3^2 = 9 and (−6)^2 = 36. Add them: 9 + 36 = 45. The distance is sqrt(45), which simplifies to sqrt(9·5) = 3√5. So the distance is 3√5.

You use the distance formula to find how far apart two points are. For points (x1, y1) = (1, 4) and (x2, y2) = (4, -2), the distance is sqrt[(x2 − x1)^2 + (y2 − y1)^2].

Compute the differences: x2 − x1 = 4 − 1 = 3, y2 − y1 = −2 − 4 = −6. Square them: 3^2 = 9 and (−6)^2 = 36. Add them: 9 + 36 = 45. The distance is sqrt(45), which simplifies to sqrt(9·5) = 3√5.

So the distance is 3√5.

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