Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

3. Functions

Intro to Functions & Their Graphs

College Algebra

3. Functions

Intro to Functions & Their Graphs

Previous problemNext problem

2: minutes

Problem 103

Textbook Question

Exercises 103–105 will help you prepare for the material covered in the next section. Let (x1, y₁) = (7, 2) and (x2, y2) = (1, −1). Find √[(x2 − x1)² + (y2 − y₁)²]. Express the - answer in simplified radical form.

Verified step by step guidance

Identify the given points: \((x_1, y_1) = (7, 2)\) and \((x_2, y_2) = (1, -1)\).

Use the distance formula: \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Substitute the given values into the formula: \(\sqrt{(1 - 7)^2 + (-1 - 2)^2}\).

Simplify the expressions inside the square root: \((1 - 7)^2 = (-6)^2\) and \((-1 - 2)^2 = (-3)^2\).

Calculate the squares and add them: \((-6)^2 + (-3)^2\), then simplify the square root.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

Key Concepts

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

Distance Formula

The distance formula is a mathematical equation used to determine the distance between two points in a Cartesian coordinate system. It is derived from the Pythagorean theorem and is expressed as d = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) and (x2, y2) are the coordinates of the two points. Understanding this formula is essential for solving problems related to distances in geometry.

Simplified Radical Form

Simplified radical form refers to the expression of a square root in its simplest terms, where no perfect square factors remain under the radical sign. For example, √8 can be simplified to 2√2. This concept is important for presenting answers in a clear and concise manner, especially in algebraic contexts where simplification is often required.

Coordinate System

A coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis), allowing for the representation of points using ordered pairs (x, y). Understanding how to plot points and interpret their coordinates is crucial for applying the distance formula and solving related problems in algebra and geometry.