Mastering the Midpoint & Distance on the Number Line
In geometry, lines have starting and ending points. Between these points, we can find the exact middle, called the midpoint, and measure how long the line is, known as the distance. This guide will explain these two concepts in simple terms. So, if you're looking to understand how to find the middle of a line or how long it is, you're in the right place!
Step-by-step Guide: Distance and Midpoint on the Number Line
Understanding the Midpoint:
The midpoint between two numbers (or points) on a number line is the number that lies exactly halfway between them. The formula to find the midpoint \(M\) between two points \(A(x_1)\) and \(B(x_2)\) is:
\(M = \frac{x_1 + x_2}{2} \)
the Concept of Distance:
The distance between two numbers (or points) on a number line is the absolute difference between them. The formula to find the distance \(D\) between two points \(A(x_1)\) and \(B(x_2)\) is:
\( D = |x_2 – x_1| \)
Examples
Example 1: Midpoint
Find the midpoint between the numbers \(4\) and \(10\) on the number line.
Solution:
Using the midpoint formula:
\( M = \frac{4 + 10}{2} \)
\( M = \frac{14}{2} \)
\( M = 7 \)
So, the midpoint is \(7\).
Example 2: Distance
Find the distance between the numbers \(-3\) and \(5\) on the number line.
Solution:
Using the distance formula:
\( D = |5 – (-3)| \)
\( D = |5 + 3| \)
\( D = 8 \)
So, the distance is \(8\) units.
Practice Questions:
- Find the midpoint between the numbers \(2\) and \(8\) on the number line.
- Calculate the distance between the numbers \(-7\) and \(3\) on the number line.
- If the midpoint between two numbers \(a\) and \(b\) is \(5\), what is the value of \(b\) given \(a = 3\)?
Answers:
- The midpoint is \(5\).
- The distance is \(10\) units.
- The value of \(b\) is \(7\).
Related to This Article
More math articles
- ACT Math- Test Day Tips
- Best Digital Writing Pads for Online Teaching in 2024
- Vectors Introduction
- Best Laptops for Students: Lenovo vs. HP vs. Dell
- Pre-Algebra Formulas
- How to Prepare for the 8th Grade STAAR Math Test?
- Can You Cheat on the ALEKS Test?
- Full-Length TSI Math Practice Test-Answers and Explanations
- How to Identify the Function from the Graph
- The Ultimate MTEL Mathematics (Elementary) (68) Course (+FREE Worksheets & Tests)
What people say about "Mastering the Midpoint & Distance on the Number Line - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.