Question

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



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 need to visualize the position of the rational numbers \( a \) and \( c \) on the number line.

1. **Statement A**: The value of \( a - c \) is positive.
- This is true if \( a \) is to the right of \( c \). If \( a > c \), then \( a - c > 0 \).

2. **Statement B**: The value of \( -a - c \) is positive.
- This would be true if both \( -a \) and \( -c \) are negative numbers with \( -a < -c \) (which translates to \( a > c \)).

3. **Statement C**: The value of \( c - a \) is negative.
- This is true if \( c \) is to the left of \( a \), meaning \( c < a \) (which implies \( c - a < 0 \)).

4. **Statement D**: The value of \( -c - a \) is negative.
- This would be true if both \( -c \) and \( -a \) are negative, meaning \( c > a \) (which implies \( -c < -a \), thus making \( -c - a < 0 \)).

Without knowing the exact positions of \( a \) and \( c \), we cannot definitively conclude which specific statement is true. However, here’s how you can analyze them based on their positions:

- If \( a > c \), then A and C are true, and B is possible but depends on the absolute values.
- If \( a < c \), then C and D are true, and A would be false.

To find the correct statement, you need to determine the relative positions of \( a \) and \( c \) on the number line. If you have that information (whether \( a \) is to the left or right of \( c \)), you can confirm which statements are true based on those positions.