Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 6

Chapter 3, Problem 6

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)

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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