Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (0, 0) and (3,-4)

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Identify the coordinates of the two points: Point 1 is (0, 0) and Point 2 is (3, -4).

Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]

Substitute the given coordinates into the formula: \[d = \sqrt{(3 - 0)^2 + (-4 - 0)^2}\]

Simplify inside the square root by calculating the differences and squaring them: \[d = \sqrt{3^2 + (-4)^2}\]

Express the distance in simplified radical form by evaluating the squares and then the square root, and finally round the result to two decimal places if needed.

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주요 개념

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Distance Formula

The distance formula calculates the length between two points in the coordinate plane. It is derived from the Pythagorean theorem and given by d = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the points.

Simplified Radical Form

Simplified radical form means expressing a square root in its simplest form by factoring out perfect squares. For example, √50 can be simplified to 5√2. This helps in presenting exact answers before rounding.

Rounding Decimal Numbers

Rounding involves approximating a number to a specified number of decimal places for simplicity. In this problem, after finding the exact distance, the result should be rounded to two decimal places to provide a practical numerical answer.