Questions: Unit 2 Quiz 2 7. Choose the best answer. The points on any line segment can be put into one-to-one correspondence with real numbers so that two selected points can have coordinates 0 and 1, and that the distance between two points is the absolute value of the difference between the corresponding numbers. The difference between the corresponding numbers is a sublement of the: □ Ruler □ Correspondence □ Segment Addition □ Coordinate

Unit 2 Quiz 2

7. Choose the best answer.

The points on any line segment can be put into one-to-one correspondence with real numbers so that two selected points can have coordinates 0 and 1, and that the distance between two points is the absolute value of the difference between the corresponding numbers. The difference between the corresponding numbers is a sublement of the:

□ Ruler
□ Correspondence
□ Segment Addition
□ Coordinate

Transcript text: Unit 2 Quiz 2 7. Choose the best answer. The points on any line segment can be put into one-to-one correspondence with real numbers so that two selected points can have coordinates 0 and 1, and that the distance between two points is the absolute value of the difference between the corresponding numbers. The difference between the corresponding numbers is a sublement of the: □ Ruler □ Correspondence □ Segment Addition □ Coordinate

Solution

Solution Steps

To solve this problem, we need to understand the concept being described. The statement is about the ability to assign real number coordinates to points on a line segment such that the distance between any two points is the absolute value of the difference of their coordinates. This concept is related to the Ruler Postulate in geometry, which states that the points on a line can be matched one-to-one with real numbers, and the distance between any two points is the absolute value of the difference of their coordinates. Therefore, the best answer is "Ruler."

Step 1: Understanding the Problem

We are given two points on a line segment, \( A \) and \( B \), with coordinates \( A = 0 \) and \( B = 1 \). The task is to determine the distance between these two points using the concept of absolute value of the difference of their coordinates.

Step 2: Calculate the Distance

The distance \( d \) between two points \( A \) and \( B \) can be calculated using the formula: \[ d = |B - A| \] Substituting the values of \( A \) and \( B \): \[ d = |1 - 0| = |1| = 1 \]

Step 3: Identify the Correct Answer

The problem also asks for the identification of the concept related to the distance calculation. The correct concept that describes the relationship between points on a line segment and real numbers is the Ruler Postulate.