Question

Rational numbers a and c are plotted on the number line.

The number line shows point A is 6 units to the left of 0 and point C is 2 units to the right of 0.

Based on the number line, which statement is true?
A.
The value of
a - c is positive.

B.
The value of
- a - c is positive.

C.
The value of
c - a is negative.

D.
The value of
- c - a is negative.

Answer 1

To determine which statement is true, we first need to identify the values of \( a \) and \( c \) based on their positions on the number line.

- Point \( A \) is 6 units to the left of 0, so:
\[ a = -6 \]

- Point \( C \) is 2 units to the right of 0, so:
\[ c = 2 \]

Now, let's analyze each statement:

**A:** The value of \( a - c \) is positive.
\[
a - c = -6 - 2 = -8 \quad \text{(negative)}
\]
So, A is false.

**B:** The value of \( -a - c \) is positive.
\[
-a - c = -(-6) - 2 = 6 - 2 = 4 \quad \text{(positive)}
\]
So, B is true.

**C:** The value of \( c - a \) is negative.
\[
c - a = 2 - (-6) = 2 + 6 = 8 \quad \text{(positive)}
\]
So, C is false.

**D:** The value of \( -c - a \) is negative.
\[
-c - a = -2 - (-6) = -2 + 6 = 4 \quad \text{(positive)}
\]
So, D is false.

The only true statement is:

**B. The value of \(-a - c\) is positive.**