Question

The expression below represents the distance between two points on a number line.

|
−
5
−
4
|

Which number line shows the two points?

A.
The number line between -9 and 8 shows point a at -5 and point b at 4.

B.
The number line between -9 and 8 shows point a at -5 and point b at -4.

C.
The number line between -9 and 8 shows point a at -9 and point b at 4.

D.
The number line between -9 and 8 shows point a at 4 and point b at 5.

Answer 1

To solve the distance expression |−5−4|, we should first interpret what it means. The expression represents the distance between the two points -5 and -4 on a number line.

The distance formula in one dimension (for two points \( a \) and \( b \)) is given by:

\[ |a - b| \]

In this case, the two points are -5 and -4, so the calculation would be:

\[ |-5 - (-4)| = |-5 + 4| = |-1| = 1 \]

Now we need to identify which of the given options represents the correct points -5 and -4.

Looking at the options:

A. Point a at -5 and point b at 4 - **Incorrect** (point b is not -4).

B. Point a at -5 and point b at -4 - **Correct** (this is the right representation of the points).

C. Point a at -9 and point b at 4 - **Incorrect** (point a is not -5).

D. Point a at 4 and point b at 5 - **Incorrect** (neither point corresponds to -5 or -4).

Therefore, the correct answer is:

**B. The number line between -9 and 8 shows point a at -5 and point b at -4.**