**Which \[2\] of the following expressions represent the distance between \[-2\] and \[1.5\]?**

\[\llap{-}3\]\[\llap{-}2\]\[\llap{-}1\]\[0\]\[1\]\[2\]\[\llap{-}2\]\[1.5\]

Choose 2 answers:

Choose 2 answers:

(Choice A)   

\[| -2 - 1.5|\]

A

\[| -2 - 1.5|\]

(Choice B)   

\[| {1.5} + 2|\]

B

\[| {1.5} + 2|\]

(Choice C)   

\[| 1.5 - 2|\]

C

\[| 1.5 - 2|\]

To determine which expressions represent the distance between \(-2\) and \(1.5\), we need to consider the definition of distance on the number line. The distance between two numbers \(a\) and \(b\) is given by \(|a - b|\) or \(|b - a|\).

Let's evaluate the given choices:

1. **Choice A:** \(| -2 - 1.5|\)  
   This represents the distance between \(-2\) and \(1.5\).  
   \(-2 - 1.5 = -3.5\), so \(|-3.5| = 3.5\).

2. **Choice B:** \(| 1.5 + 2|\)  
   This does not represent the distance between \(-2\) and \(1.5\) because the expression adds the two numbers instead of subtracting them.  
   \(1.5 + 2 = 3.5\), so \(|3.5| = 3.5\), but this is not the correct form for calculating distance.

3. **Choice C:** \(| 1.5 - 2|\)  
   This expression involves subtracting \(2\) from \(1.5\), which does not directly give the distance between \(-2\) and \(1.5\).  
   \(1.5 - 2 = -0.5\), so \(|-0.5| = 0.5\), but this does not represent the distance between the two original points.

The correct answers are:

- **Choice A:** \(| -2 - 1.5|\) (This correctly represents the distance between \(-2\) and \(1.5\).)
- **Choice C:** \(|1.5 - (-2)| = |1.5 + 2|\) (This was not listed directly, but it would be the correct distance expression if given. Unfortunately, it's not present, so only Choice A directly applies.)

However, the problem as presented seems to require careful reading, as it implies that two answers should represent the distance, but in reality, only Choice A directly corresponds to the correct distance. 

Would you like any further details or have any questions?

Here are 5 related questions:

1. What is the distance between \(-3\) and \(4.5\)?
2. How would you represent the distance between \(0\) and \(5\) using an absolute value expression?
3. Calculate the distance between \(7.2\) and \(-1.3\).
4. Find the distance between \(-4\) and \(-2\).
5. What is the distance between \(1.5\) and \(2\)?

**Tip**: Distance between two points on a number line is always positive and can be calculated using absolute value!

Explore how to calculate the distance between numbers using absolute value. This example problem evaluates the distance between -2 and 1.5 on the number line. Learn the concept of absolute value and its application in calculating distances. Suitable for Grades 6-8 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation