Points p and q are negative integers plotted on a number line.
If |p| > |q|, which statement is true?
A.
Point p is further from 0 than point q, and to the left of point q.
B.
Point p is closer to 0 than point q, and to the left of point q.
C.
Point p is further from 0 than point q, and to the right of point q.
D.
Point p is closer to 0 than point q, and to the right of point q.
|p| > |q| means that p is more negative than q
A. looks good
The answer would be A.
If |p| > |q|, it means that the absolute value of p is greater than the absolute value of q. Since p and q are negative integers plotted on a number line, it means that p is further from 0 than q.
So, the correct statement would be:
A. Point p is further from 0 than point q, and to the left of point q.
To answer this question, you need to understand the concept of absolute value and the placement of negative integers on a number line.
The absolute value of a number is its distance from 0 on the number line, regardless of its sign. For example, the absolute value of -5 is 5, and the absolute value of -3 is 3.
Given that |p| > |q|, it means that the absolute value of p is greater than the absolute value of q.
When plotting negative integers on a number line, the numbers to the left are smaller (closer to 0) and the numbers to the right are larger (farther from 0).
Now let's analyze the statement options:
Option A: Point p is further from 0 than point q, and to the left of point q.
This statement contradicts the fact that |p| > |q|. If p is further from 0 than q, it means that the absolute value of p is greater than the absolute value of q, which is what we are given. Therefore, option A is incorrect.
Option B: Point p is closer to 0 than point q, and to the left of point q.
This statement is consistent with the fact that |p| > |q|. If p is closer to 0 than q and both points are to the left, it means that the absolute value of p is smaller than the absolute value of q. Therefore, option B is incorrect.
Option C: Point p is further from 0 than point q, and to the right of point q.
This statement contradicts the fact that |p| > |q|. If p is further from 0 than q, it means that the absolute value of p is greater than the absolute value of q, which is what we are given. Therefore, option C is incorrect.
Option D: Point p is closer to 0 than point q, and to the right of point q.
This is the correct statement. If p is closer to 0 than q and both points are to the right, it means that the absolute value of p is smaller than the absolute value of q. Therefore, option D is the correct answer.
Therefore, the correct statement is:
D. Point p is closer to 0 than point q, and to the right of point q.