0<r<S<t On the number line, the coordinate of point P is t-s, and the coordinate of point Q is r-1. Quantity A: The distance between points P and Q on the number line Quantity B: 2t - s - r

Rationale

The two quantities are equal.

To find the distance between points P and Q, we calculate the absolute difference of their coordinates, which equals ( |(t - s) - (r - 1)| ). Simplifying this expression leads to the conclusion that the distance is equal to ( 2t - s - r ), making Quantity A and Quantity B equal.

A (Quantity A is greater.) YOUR ANSWER

This option suggests that the distance between points P and Q exceeds the expression ( 2t - s - r ). However, the calculations show that both quantities are indeed equal, so this statement is incorrect.

B (Quantity B is greater.) YOUR ANSWER

This choice implies that ( 2t - s - r ) is greater than the distance between points P and Q. However, as demonstrated, the distance simplifies to exactly ( 2t - s - r ), making this assertion false.

C (The two quantities are equal.) CORRECT

This is the correct assertion since the calculation of the distance between P and Q directly leads to the expression ( 2t - s - r ). Hence, both quantities are equal.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

This option suggests that the relationship between the two quantities is indeterminate. However, the calculations confirm that the relationship is clear and defined, thereby making this choice incorrect.

Conclusion

The analysis indicates that the distance between points P and Q directly corresponds to the expression ( 2t - s - r ), confirming that both quantities are equal. Therefore, the correct answer is that the two quantities are equal, demonstrating a clear relationship based on the given coordinates.

0<r<S<t On the number line, the coordinate of point P is t-s, and the coordinate of point Q is r-1. Quantity A: The distance between points P and Q on the number line Quantity B: 2t - s - r

The two quantities are equal.

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