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A midpoint is half way, so it divides the segment KM into two equal halves. In this problem segment KL will be equal to segment LM.

2x+1=3x-4
Subtract 2x from both sides
1=x-4
Add 4 to both sides
5=x

KL (2x+1)
Substitute the answer for x in expression
=2(5)+1
=10+1
=11

LM (3x-4)
=3(5)-4
=15-4
=11

KM
=KL+LM
=11+11
=22

The answer is D) 11, 11, 22

Hope this helps! :)
MrRoyal

The midpoint of a line divides the line into equal segments

The values of the segments are:

  • [tex]KL = 11[/tex].
  • [tex]LM = 11[/tex].
  • [tex]KM = 22[/tex]

The parameters are given as:

[tex]KL = 2x + 1[/tex]

[tex]LM = 3x -4[/tex]

Since L is the midpoint, then:

[tex]KL = LM[/tex]

So, we have:

[tex]2x + 1 = 3x - 4[/tex]

Collect like terms

[tex]3x - 2x = 1+ 4[/tex]

[tex]x = 5[/tex]

The value of KL is

[tex]KL = 2x + 1[/tex]

[tex]KL = 2 \times 5 + 1[/tex]

[tex]KL = 11[/tex]

Recall that:

[tex]KL = LM[/tex]

So:

[tex]LM = 11[/tex]

The value of KM is the sum of both segments

[tex]KM = 11 +11[/tex]

[tex]KM = 22[/tex]

Read more about midpoints at:

https://brainly.com/question/2441957

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