Question

What is the distance between -a and 0

Answer 1

Answer

Distance is $|-a|=\begin{cases} &-a (a\geq 0) \\ &a (a<0) \end{cases}$.

Solution

A distance between two lines is a absolute value.

Because distance is a non-negative value.

After moving the distance, we end up in a greater number.

Total Cases

• $-a$ can be either positive, 0, or negative.

Case 1. $-a<0$

$-a+\mathrm{Distance}=0$

$\therefore\mathrm{Distance}=a$

Case 2. $-a=0$

$\therefore \mathrm{Distance}=0$

Case 3. $-a>0$

$0+\mathrm{Distance}=-a$

$\therefore\mathrm{Distance}=-a$

It's all positive value, so it can be written as $|-a|$.

More information

On the number line, adding the numbers is moving to the right.

0 is called the origin.

The absolute value is the value without a negative sign.

Verification

Distance between -1 and 0 is 1, or $|1|=1$(True).

Distance between 1 and 0 is 1, or $|-1|=1$(True).