Question

e is the midpoint of df. find the value of x and each missing length. #9: x = ____ #9: de = __ #9: ef = ____

Explanation:

Step1: Set up equation using mid - point property

Since E is the mid - point of DF, then $DE = EF$. So we set up the equation $3x + 2=5x - 20$.

Step2: Solve for x

Subtract $3x$ from both sides: $3x+2 - 3x=5x - 20-3x$, which simplifies to $2 = 2x-20$. Then add 20 to both sides: $2 + 20=2x-20 + 20$, giving $22 = 2x$. Divide both sides by 2: $\frac{22}{2}=\frac{2x}{2}$, so $x = 11$.

Step3: Find DE

Substitute $x = 11$ into the expression for DE: $DE=3x + 2=3\times11 + 2=33 + 2=35$.

Step4: Find EF

Since $EF = DE$, then $EF = 35$.

Step5: Find DF

$DF=DE + EF=35+35 = 70$.

Answer:

$x = 11$
$DE = 35$
$EF = 35$
$DF = 70$