segment tq is 26 units long. what is the length of qv?

8 units
26 units
31 units
32 units

Question

segment tq is 26 units long. what is the length of qv?

8 units
26 units
31 units
32 units

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Perpendicular Bisector Theorem" ], "new_concepts": [], "current_concepts": [ "Perpendicular Bisector Theorem", "Rhombus Properties" ] } ## Set up the equation using the Perpendicular Bisector Theorem $$ \begin{aligned} &SR = RQ \quad \text{and} \quad SQ \perp TV \ &ST = TQ \implies 3x + 2 = 26 \ &SV = QV \implies 4x - 1 = QV \end{aligned} $$ ## Solve for x $$ \begin{aligned} 3x + 2 &= 26 \ 3x &= 24 \ x &= 8 \end{aligned} $$ ## Calculate the length of QV $$ \begin{aligned} QV &= 4x - 1 \ QV &= 4(8) - 1 \ QV &= 32 - 1 \ QV &= 31 \end{aligned} $$

8 units

26 units

31 units

32 units

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Bisector Theorem" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the equation using the Perpendicular Bisector Theorem

Solve for x

Calculate the length of QV

Answer: