Question

question 5

\\(f\\) is the midpoint of \\(\overline{gh}\\).

find \\(x\\) and the length of \\(\overline{fh}\\).

not all answer choices will be used

\\(g\\) \\(5x + 11\\) \\(f\\) \\(12x - 17\\) \\(h\\)

answer bank
4, 31, 3, 19

Explanation:

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<reasoning>

Apply the midpoint definition

Using the Segment Midpoint Definition knowledge point
\[
GF = FH
\]

Set up the equation

Using the Geometric Segment Solving knowledge point
\[
5x + 11 = 12x - 17
\]

Solve for x

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 11 + 17 &= 12x - 5x \\ 28 &= 7x \\ x &= 4 \end{aligned}$$

\]

Calculate the length of FH

Using the Geometric Segment Solving knowledge point
\[

$$\begin{aligned} FH &= 12(4) - 17 \\ FH &= 48 - 17 \\ FH &= 31 \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 4\)
\(FH = 31\)
</answer>

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Answer:

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</pre_analysis>

<reasoning>

Apply the midpoint definition

Using the Segment Midpoint Definition knowledge point
\[
GF = FH
\]

Set up the equation

Using the Geometric Segment Solving knowledge point
\[
5x + 11 = 12x - 17
\]

Solve for x

Using the Linear Equations knowledge point
\[

$$\begin{aligned} 11 + 17 &= 12x - 5x \\ 28 &= 7x \\ x &= 4 \end{aligned}$$

\]

Calculate the length of FH

Using the Geometric Segment Solving knowledge point
\[

$$\begin{aligned} FH &= 12(4) - 17 \\ FH &= 48 - 17 \\ FH &= 31 \end{aligned}$$

\]
</reasoning>

<answer>
\(x = 4\)
\(FH = 31\)
</answer>

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