Math Problem Statement
Solution
The question asks to identify the segment bisector of segment , where , , and are points on a line segment. It also provides the following information:
- The distance from to is
- The distance from to is
Since a segment bisector divides a segment into two equal parts, we can set the two distances equal to each other:
Let's solve this equation to find :
Subtract from both sides:
Now that we know , we can calculate the lengths of and :
Since both lengths are equal, point is the midpoint of , and it bisects the segment.
Thus, the correct answer is:
- is the segment bisector of .
Would you like further details or have any questions about this? Here are some related questions for practice:
- If and , find the value of for which bisects .
- How do you determine if a point is the midpoint of a line segment?
- What is the formula for calculating the midpoint between two points on a coordinate plane?
- If the total length of segment is 60, what is the length of each bisected part if is the midpoint?
- In a triangle, how can you determine if a median also serves as the segment bisector?
Tip: A segment bisector always cuts a segment into two equal parts. The midpoint formula on a coordinate plane is a useful tool for verifying this division.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Segment Bisectors
Geometry
Formulas
7x + 5 = 8x
Theorems
Segment Bisector Theorem
Suitable Grade Level
Grades 6-8
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