Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (3.5, 8.2) and (-0.5, 6.2)

Verified step by step guidance

1. Identify the coordinates of the two points: Point 1 is (3.5, 8.2) and Point 2 is (-0.5, 6.2).
2. Recall the distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\): \[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\]
3. Substitute the given coordinates into the formula: \[d = \sqrt{(-0.5 - 3.5)^2 + (6.2 - 8.2)^2}\]
4. Simplify the expressions inside the parentheses: Calculate \((-0.5 - 3.5)\) and \((6.2 - 8.2)\), then square each result.
5. Add the squared values and take the square root of the sum to find the distance. If possible, simplify the radical before rounding to two decimal places.

Key Concepts

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. This helps present answers in an exact form before approximating decimals, ensuring clarity and precision in mathematical solutions.

Rounding Decimals

Rounding decimals involves approximating a number to a specified number of decimal places. In this problem, answers are rounded to two decimal places, which means keeping two digits after the decimal point and adjusting the last digit based on the next digit.