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Anit [1.1K]
3 years ago
15

E is the midpoint of DF⎯⎯⎯⎯⎯, DE=6x+1 and EF=7x−4. Find DE, EF, and DF

Mathematics
1 answer:
grandymaker [24]3 years ago
8 0

DE is 31 units, EF is 31 units and DF is 62 units

Step-by-step explanation:

A mid-point of a line segment

  • Divides it into two congruent parts
  • The length of each part is half the length of the line segment

∵ E is the mid-point of segment DF

- That means E divides DF into two parts DE and EF and the

   lengths of them are equal

∴ DE ≅ EF

∵ DE = 6x + 1

∵ EF = 7x - 4

- Equate them

∴ 6x + 1 = 7x - 4

- Add 4 to both sides

∴ 6x + 5 = 7x

- Subtract 6x from both sides

∴ 5 = x

Substitute the value of x in DE and EF to find their length

∵ DE = 6(5) + 1

∵ DE = 30 + 1

∴ DE = 31 units

∵ EF = 7(5) - 4

∴ EF = 35 - 4

∴ EF = 31 units

∵ DF = DE + EF

∴ DF = 31 + 31

∴ DF = 62 units

DE is 31 units, EF is 31 units and DF is 62 units

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

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