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PsychicPhantom
When there is a midpoint in a line segment, the two segments that are then produced have to be equal. So that means that because E is a midpoint of DF, DE=EF.
Set up the equation.
DE=EF
2x+4=3x+1
Then solve for x.
x=3
Then plug it back in the equation to find DE and EF.
DE=2x+4=2(3)+4=10
Because DE=EF then EF is also 10.
DF is made from the addition of DE and EF so DF is twice EF.
DF= 20

DE= 10, EF= 10, DF= 20

Hope this helps.
abidemiokin

The length of DE, EF and, DF are 10, 10, and 20 respectively.

The midpoint is a point on the line that bisects or divides such a line into two equal parts.

If E is the midpoint of DF, this means that point E divides the line DF into equal parts.

The following is therefore true

  1. DE + EF = DF
  2. DE = EF

According to the first equation:

DF = 2x + 4 + 3x + 1

DF = 5x + 5

Based on equation 2:

DE = EF

2x  + 4 = 3x + 1

2x - 3x  = 1-4

-x = -3

x = 3

Get DE:

DE = 2x + 4

DE = 2(3) + 4

DE = 6 + 4

DE = 10

Since DE = EF

EF = 1

Get the measure of DF

DF = DE + EF

DF = 10 + 10

DF = 20

This shows that the length of DE, EF and, DF are 10, 10, and 20 respectively.

Learn more here: https://brainly.com/question/16764541  andhttps://brainly.com/question/17294517

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