To solve the problem, we need to analyze the given condition and the statements in the context of negative integers.
The notation |p| and |q| represents the absolute values of p and q, respectively. Since p and q are both negative integers, their absolute values are positive. The condition |p| > |q| means that the absolute value of p is greater than the absolute value of q.
This implies that:
- If |p| > |q|, then p must be a larger negative number than q. For instance, if p = -4 and q = -2, then |p| = 4 and |q| = 2, satisfying |p| > |q|.
Next, we identify how these numbers are positioned on the number line:
- Negative integers are positioned to the left of zero. The further away from zero (i.e., the more negative the number), the further left on the number line it will be.
- Since |p| > |q| means p is further away from zero (more negative) than q, it follows that p is to the left of q on the number line.
Now, let's evaluate the statements provided:
A. Point p is further from 0 than point q, and to the right of point q. (False, because p is to the left of q.) B. Point p is closer to 0 than point q, and to the right of point q. (False, because p is further from 0 and is to the left of q.) C. Point p is closer to 0 than point q, and to the left of point q. (False, because p is further from 0.) D. Point p is further from 0 than point q, and to the left of point q. (True, this is correct.)
Thus, the correct statement is:
D. Point p is further from 0 than point q, and to the left of point q.