Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 7

Chapter 3, Problem 7

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

Verified step by step guidance

Identify the coordinates of the two points: Point 1 is \((-2, -6)\) 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: \[d = \sqrt{(3 - (-2))^2 + (-4 - (-6))^2}\]

Simplify inside the parentheses: \[d = \sqrt{(3 + 2)^2 + (-4 + 6)^2}\] which becomes \[d = \sqrt{5^2 + 2^2}\]

Calculate the squares and write the expression under the square root: \[d = \sqrt{25 + 4}\] Then simplify the radical if possible, and finally round the result to two decimal places.

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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 is given by √[(x2 - x1)² + (y2 - y1)²]. This formula helps find the straight-line distance between points (x1, y1) and (x2, y2).

Simplifying Radical Expressions

Simplifying radicals involves expressing a square root in its simplest form by factoring out perfect squares. This makes the answer more exact and easier to interpret before rounding. For example, √50 can be simplified to 5√2 by factoring 50 into 25 × 2.

Rounding Decimal Numbers

Rounding is the process of approximating a number to a specified number of decimal places for clarity or practicality. In this problem, after simplifying the radical, the distance should be rounded to two decimal places to provide a clear, usable numerical answer.

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Related Practice

Textbook Question

Determine whether each equation defines y as a function of x. 2x + y^2 = 6

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Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (2, −3) and perpendicular to the line whose equation is y = (1/5)x + 6

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Find f(g(x)) and g (f(x)) and determine whether each pair of functions ƒ and g are inverses of each other. f(x) = 3/(x-4) and g(x) = (3/x) + 4

Textbook Question

Use the graph of y = f(x) to graph each function g.

g(x) = f(-x)

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Textbook Question

Find the slope of the line passing through each pair of points or state that the slope is undefined. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (4, -1) and (3, −1)

Textbook Question

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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