Given the number line with points A, B, and O and the relationships between them as shown in the image, we can analyze each statement based on the positioning of these points.

Observations:

• O is the origin, so its coordinate is 0.
• A is to the left of B, and both are to the left of O, meaning both a and b are negative values.
• Since A is to the left of B, we have a<b<0

Let's now evaluate each of the options:

• (A) |a| < |b|:
  • This is incorrect because A is farther from the origin than B, meaning .
• (B) a \times b < 0:
  • This is incorrect because both a and b are negative numbers, and the product of two negative numbers is positive.
• (C) a - b < 0:
  • This is correct because , so subtracting a larger number (b) from a smaller number (a) will result in a negative value.
• (D) a + b > 0:
  • This is incorrect because both a and b are negative, and the sum of two negative numbers is always negative.

Correct Answer:

(C) a - b < 0.

根據數線上的 A、B 和 O 三個點及它們之間的關係,我們可以分析每個陳述。

觀察:

• O 是原點,其座標為 0。