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

Question

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.