Question

How do you find the distance between $9$ and $ - 12$ using absolute values? $?$

Answer 1

Hint: In this question, we are going to find distance between two numbers by using absolute value.
First we are going to find the distance by using the distance between two points formula.
We get a value by substituting the formula and that is the absolute value of the numbers.
Absolute value must be non negative so, write the obtained result in a positive sign.
Hence, we get the required result.

Complete step-by-step solution:
In this we are going to find distance between two numbers using absolute value,
First, we are going to use the formula,
The distance between two numbers is the absolute value of the difference of the numbers.
The distance between two numbers $x$and $y$can be written as $\left| {x - \left. y \right|} \right..$
Subtract $9$on the number line from the number $ - 12$ we can get the required solution.
Distance between two points= $\left| {9 - \left. {\left( { - 12} \right)} \right|} \right.$
$ = \left| {9 + \left. {12} \right|} \right.$
Distance between two points $ = \left| {\left. {21} \right|} \right.$
Obtain the absolute value of the number line difference.
Absolute value basically measures how far the number is from zero.
In mathematics, the absolute value or modulus of a real number $X$ , denoted $\left| X \right|$ , is the non-negative value of $X$ without any regard to its sign.
For this, the absolute value either $21$ or $ - 21$ that is $\left| {\left. {21} \right|} \right.$ or $ - \left| {\left. {21} \right|} \right.$ is $21$ .

Therefore, the distance between the two numbers $9$ and $ - 12$ is $21$.

Note: A simple way to calculate distance between two numbers on a number line is to count every number between them. A faster way is to find the distance by taking the absolute value of the difference of those numbers. The absolute value is fundamentally about the distance between two values, depending on the expression contained within the absolute value sign.
The absolute value as “distance from zero” is used to define the absolute difference between arbitrary real numbers, the standard metric on the real numbers.
Notice that you don’t need to know which number is greater (if the numbers are different) to find the distance between them. And of course, if two numbers are equal, then the distance between them is zero.