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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.

1 answer

Let's determine the values of \( A \) and \( C \) based on the information given:

  • 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 evaluate each statement one by one:

A.

  • The value of \( A - C \) is: \[ A - C = -6 - 2 = -8 \] This is negative, so statement A is false.

B.

  • The value of \( -A - C \) is: \[ -A - C = -(-6) - 2 = 6 - 2 = 4 \] This is positive, so statement B is true.

C.

  • The value of \( C - A \) is: \[ C - A = 2 - (-6) = 2 + 6 = 8 \] This is positive, so statement C is false.

D.

  • The value of \( -C - A \) is: \[ -C - A = -2 - (-6) = -2 + 6 = 4 \] This is positive, so statement D is false.

Therefore, the only true statement is:

B. The value of -A - C is positive.