Math Problem Statement

Identify the segment bisector of JK. The distances are JM = 7x + 5 and MK = 8x. The task is to find the point that bisects segment JK.

Solution

The question asks to identify the segment bisector of segment JKJK, where JJ, MM, and KK are points on a line segment. It also provides the following information:

  • The distance from JJ to MM is 7x+57x + 5
  • The distance from MM to KK is 8x8x

Since a segment bisector divides a segment into two equal parts, we can set the two distances equal to each other:

7x+5=8x7x + 5 = 8x

Let's solve this equation to find xx:

7x+5=8x7x + 5 = 8x

Subtract 7x7x from both sides:

5=x5 = x

Now that we know x=5x = 5, we can calculate the lengths of JMJM and MKMK:

  1. JM=7x+5=7(5)+5=35+5=40JM = 7x + 5 = 7(5) + 5 = 35 + 5 = 40
  2. MK=8x=8(5)=40MK = 8x = 8(5) = 40

Since both lengths are equal, point MM is the midpoint of JKJK, and it bisects the segment.

Thus, the correct answer is:

  • MM is the segment bisector of JKJK.

Would you like further details or have any questions about this? Here are some related questions for practice:

  1. If JM=3x+10JM = 3x + 10 and MK=5xMK = 5x, find the value of xx for which MM bisects JKJK.
  2. How do you determine if a point is the midpoint of a line segment?
  3. What is the formula for calculating the midpoint between two points on a coordinate plane?
  4. If the total length of segment JKJK is 60, what is the length of each bisected part if MM is the midpoint?
  5. 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