Final answer:
The question involves determining which statements about distances of points from the origin on a number line are true. The distances of c and x are equal. The statement (b) is true.
Step-by-step explanation:
(a) |a| > |x| is false. The distance between two points on the number line is the absolute value of the difference between their distances from the origin. So, |a| is the distance of point a from the origin, and |x| is the distance of point x from the origin.
Therefore, we cannot determine the relationship between |a| and |x| based on the given information.
(b) c = x is true. Since c and x have the same distance from the origin, their distances are equal.
(c) |c| = |x| is false. The distances of c and x are equal, but their absolute values may not be equal, as the distances can be negative.
(d) a > h is false. The relationship between a and h cannot be determined based on the given information.
So, the statement (b) is true.
Assuming a number line where:
a is the distance of point a from the origin, x is the distance of point x from the origin, c is the distance of point c from the origin, h is the distance of point h from the origin.
Which of the following statements are true based on the number line above? (Select all that apply)
a) |a| > |x|
b) c = x
c) |c| = |x|
d) a > h