Math Problem Statement

Given segment XZ and point Y that lies on XZ, if XY = 47 and YZ = 4, find XZ. Also, what is the length of segment SR from the number line?

Solution

Let's solve Question 3 and Question 4 step by step.


Question 3:

We are given:

  • XY=47XY = 47
  • YZ=4YZ = 4
  • YY lies on XZXZ, meaning the total segment XZXZ is composed of XY+YZXY + YZ.

To find XZXZ: XZ=XY+YZ=47+4=51XZ = XY + YZ = 47 + 4 = 51 None of the provided options includes 5151, so the correct answer is: "None of these are correct."


Question 4:

We need to determine the length of segment SRSR from the number line.

From the figure:

  • SS is at 6-6
  • RR is at 5-5

The length of SRSR is the absolute difference between the two points: SR=RS=5(6)=5+6=1=1SR = |R - S| = |-5 - (-6)| = |-5 + 6| = |1| = 1

The correct answer is: 1


Summary of Answers:

  • Question 3: None of these are correct.
  • Question 4: 1.

Do you need more details for any step? Let me know!


Related Questions:

  1. How do you calculate segment lengths using a number line?
  2. What is the segment addition postulate, and how is it applied?
  3. How can you verify the midpoint of a segment?
  4. How do you find the length of overlapping segments?
  5. What are the properties of collinear points on a line segment?

Tip: Always check if a given segment is composed of smaller parts to use the addition postulate.

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Math Problem Analysis

Mathematical Concepts

Segment Addition Postulate
Number Line Geometry
Absolute Value

Formulas

Segment Addition Postulate: XZ = XY + YZ
Absolute Difference Formula: |R - S|

Theorems

Segment Addition Postulate

Suitable Grade Level

Grades 6-8