Answer:
<u>Basic Concept used:</u>
Since D is the mid-point of EF,
ED will be equal to DF since D is in the middle of the line segment
We are given the following values for ED and DF
ED = 4x + 6 and DF = 7x - 9
<u>Solving for x:</u>
Since ED = DF (D is the mid point)
4x + 6 = 7x - 9
9 + 6 = 7x - 4x
15 = 3x
x = 5
<u>Finding the values of ED , DF and EF:</u>
we know that x = 5 (from the last section)
we are given the following values of the line segments:
ED = 4x + 6
DF = 7x - 9
EF (ED + DF) = (4x + 6) + (7x - 9)
Replacing x with 5 in each of these equations:
ED = 4(5) + 5 = 26
DF = 7(5) - 9 = 26
EF = (4(5) + 6) + (7(5)-9) = 26 + 26 = 52