Q. 10 - Precalculus Enhanced with Graphing Utilities

Question

True or False The distance between two points is sometimes a negative number.

Step-by-Step Solution

Answer

The given statement is false.

Step 1. Given information.

The given statement is:

The distance between two points is sometimes a negative number.

We need to check whether the given statement is true or false.

Step 2. Determine whether the statement is true or false.

If P and Q are two points on a real number line with coordinates $a$ and $b$, respectively, the distance between P and Q, denoted by $d(P,Q)$, is:

$d(P,Q)=\left|b-a\right|$

The modulus sign represents that the distance between two points is always a positive number and it cannot be a negative number.

Step 3. Conlusion.

The given statement is false.