Question

Which numbers are located the same number of units from Point A on the number line?

A) 5 and 3
B) -17 and 1
C) 3 and 4
D) 7 and 4
E) -1 and -1

Answer 1

The numbers located the same number of units from Point A on the number line are 5 and 3 (Option A).

Step-by-step explanation:

To determine which numbers are equidistant from a given point on the number line, we can calculate the absolute differences between each number and the given point. In this case, if Point A is our reference point, the absolute differences are as follows:

A) |A - 5| = |A - 3| = 2

B) |A - (-17)| = |A - 1| = 18

C) |A - 3| = |A - 4| = 1

D) |A - 7| = |A - 4| = 3

E) |-1 - A| = |-1 - (-1)| = 0

The numbers with the same absolute difference from Point A are 5 and 3, both having an absolute difference of 2. Therefore, (option A) 5 and 3 are located the same number of units from Point A on the number line.

Understanding the concept of absolute difference is fundamental in comparing distances on a number line. It involves finding the numerical value of the separation between two points, regardless of their direction. In this context, it helps identify which numbers share the same distance from Point A, providing a clear understanding of their relative positions on the number line.