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

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1:53 minutes

Problem 28

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (7√3, −6) and (3√3, −2)

Verified step by step guidance

Identify the formula for the midpoint of a line segment, which is given by \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \).

Substitute the given endpoints into the formula: \( x_1 = 7\sqrt{3}, y_1 = -6, x_2 = 3\sqrt{3}, y_2 = -2 \).

Calculate the x-coordinate of the midpoint: \( \frac{7\sqrt{3} + 3\sqrt{3}}{2} \).

Calculate the y-coordinate of the midpoint: \( \frac{-6 + (-2)}{2} \).

Combine the results to express the midpoint as an ordered pair.

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Key Concepts

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

Midpoint Formula

The midpoint of a line segment in a coordinate plane is calculated using the midpoint formula, which is given by M = ((x1 + x2)/2, (y1 + y2)/2). This formula averages the x-coordinates and the y-coordinates of the endpoints to find the point that is exactly halfway between them.

Coordinate System

A coordinate system is a two-dimensional plane defined by an x-axis (horizontal) and a y-axis (vertical). Each point in this system is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding this system is crucial for accurately plotting points and calculating distances or midpoints.

Square Root Properties

Square root properties are essential when dealing with expressions involving square roots, such as √3. These properties help simplify calculations and understand the numerical values of expressions. For example, knowing that √3 is approximately 1.732 can aid in estimating the coordinates when applying the midpoint formula.