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

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

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Segment Midpoint Definition", "Geometric Segment Solving", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Segment Midpoint Definition", "Geometric Segment Solving", "Linear Equations" ] } ## 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 $$ \begin{aligned} FH &= 12(4) - 17 \ FH &= 48 - 17 \ FH &= 31 \end{aligned} $$ $x = 4$ $FH = 31$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Segment Midpoint Definition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Apply the midpoint definition

Set up the equation

Solve for x

Calculate the length of FH

Answer: