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In the diagram of AUVT below, A is the midpoint of UV, B is the midpoint of UW, C is the midpoint of VW, and AB and AC are drawn. U 3x + 1 B В A V C W -7x - 3- If VW = 7x-3 and AB = 3x +1, what is the length of VC? - Answer: VC Submit Answer

In The Diagram Of AUVT Below A Is The Midpoint Of UV B Is The Midpoint Of UW C Is The Midpoint Of VW And AB And AC Are Drawn U 3x 1 B В A V C W 7x 3 If VW 7x3 A class=

Answer :

As A, B and C are midpoints, and AB is parallel to VW you have:

[tex]\begin{gathered} VW=VC+CW \\ VC=CW \\ VC=\frac{VW}{2} \\ \\ AB=\frac{1}{2}VW \\ \\ AB=VC \end{gathered}[/tex]

AB is the half of VW:

[tex]\begin{gathered} AB=3x+1 \\ VW=7x-3 \\ \\ 3x+1=\frac{7x-3}{2} \end{gathered}[/tex]

You use the equation above to find the value of x:

[tex]\begin{gathered} 2(3x+1)=7x-3 \\ 6x+2=7x-3 \\ 6x-7x=-3-2 \\ -x=-5 \\ x=5 \end{gathered}[/tex]

As you have the value of x and you know that VC is equal to AB:

[tex]\begin{gathered} AB=3x+1 \\ VC=3x+1 \\ \\ x=5 \\ \\ VC=3(5)+1 \\ VC=15+1 \\ VC=16 \end{gathered}[/tex]Then, the lenght of VC is 16 units

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