Question

point n is the midpoint of segment fg and fg = 2x + 4. select the geometric set up and the algebraic set up that would represent ng. □ fg = ng and fg + ng = fn □ x + 2 = 2x + 4 □ 2(fg) = ng □ 2(2x + 4) = 4x + 8 □ \\(\frac{1}{2}(2x + 4) = x + 2\\) □ \\(\frac{1}{2}(fg) = ng\\)

Explanation:

Step1: Recall Midpoint Definition

A midpoint of a segment divides it into two equal parts. So, \( FN = NG \) and \( FG = FN + NG = 2 \cdot NG \) (or \( NG=\frac{1}{2}FG \)).

Step2: Analyze Geometric Set Up

• For geometric setup, since \( N \) is midpoint, \( \frac{1}{2}(FG)=NG \) is correct (as midpoint divides the segment into two equal parts, so half of \( FG \) is \( NG \)).
• The other geometric options: \( FG = NG \) is wrong (as \( FG \) is the whole segment, \( NG \) is half), \( 2(FG)=NG \) is wrong (would make \( NG \) longer than \( FG \)).

Step3: Analyze Algebraic Set Up

Given \( FG = 2x + 4 \), using \( NG=\frac{1}{2}FG \), substitute \( FG \): \( \frac{1}{2}(2x + 4)=x + 2 \). So this algebraic setup is correct.

• Other algebraic options: \( x + 2 = 2x + 4 \) would imply \( NG = FG \) (wrong), \( 2(2x + 4)=4x + 8 \) is \( 2FG \) (not related to \( NG \)).

Answer:

Geometric Set Up: \(\frac{1}{2}(FG) = NG\)
Algebraic Set Up: \(\frac{1}{2}(2x + 4) = x + 2\)