Answer :
The value of EC calculated from the mid-point formula is [tex]17[/tex].
Given:
Segment CD
CD = [tex]18x-2[/tex]
E is the mid-point of CD.
ED= [tex]7x+3[/tex]
To calculate EC, Use the Mid-point formula.
As E is the Mid-point it divides CD into two equal parts.
One part is CE and the other is ED
As per the question:
CD = 2ED
EC=ED
Substitute the value of CD and ED:
[tex]18x-2 =7x+3[/tex]
Solve for [tex]x[/tex]:
Add like and unlike terms, Isolate [tex]x[/tex] on one side of the equation:
[tex]18x-7x = 3+2[/tex]
[tex]11x= 5[/tex]
[tex]x= \dfrac{5}{11}[/tex]
Now, Put the value of [tex]x[/tex] in ED to find EC
ED= [tex]7(2)+ 3[/tex]
ED = [tex]17[/tex]
EC = [tex]17[/tex]
Learn more about Mid-point here:
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