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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1:08 minutes

Problem 19

Textbook Question

In Exercises 19–30, find the midpoint of each line segment with the given endpoints. (6, 8) and (2, 4)

Verified step by step guidance

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

Assign the coordinates of the endpoints to variables: \( x_1 = 6, y_1 = 8, x_2 = 2, y_2 = 4 \).

Substitute the values into the midpoint formula: \( \left( \frac{6 + 2}{2}, \frac{8 + 4}{2} \right) \).

Simplify the expressions inside the parentheses: \( \left( \frac{8}{2}, \frac{12}{2} \right) \).

Calculate the final simplified values for the midpoint coordinates.

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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 formula is used to find the point that is exactly halfway between two given points in a coordinate plane. It is calculated using the formula M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of the endpoints. This formula provides a straightforward method to determine the average of the x-coordinates and the y-coordinates of the endpoints.

Coordinate Plane

A coordinate plane is a two-dimensional surface formed by the intersection of a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on this plane is represented by an ordered pair (x, y), where 'x' indicates the horizontal position and 'y' indicates the vertical position. Understanding the coordinate plane is essential for visualizing and solving problems involving points and lines.

Ordered Pairs

Ordered pairs are pairs of numbers used to represent the coordinates of a point in a two-dimensional space. The first number corresponds to the x-coordinate, and the second number corresponds to the y-coordinate. In the context of the given question, the endpoints (6, 8) and (2, 4) are ordered pairs that define specific locations on the coordinate plane, which are crucial for applying the midpoint formula.