in the diagram, the length of segment bc is 23 units. what is the length of segment dc?

13 units
18 units
33 units
46 units

Question

in the diagram, the length of segment bc is 23 units. what is the length of segment dc?

13 units
18 units
33 units
46 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", "Geometric Properties" ] } ## Equate segment lengths using perpendicular bisector properties $$ \begin{aligned} &AB = BC \ &2x + 7 = 23 \ &2x = 16 \ &x = 8 \end{aligned} $$ ## Calculate the length of segment AD $$ \begin{aligned} &AD = 4x + 1 \ &AD = 4(8) + 1 \ &AD = 33 \end{aligned} $$ ## Determine the length of segment DC $$ \begin{aligned} &DC = AD \ &DC = 33 \end{aligned} $$

13 units

18 units

33 units

46 units

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

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QUESTION IMAGE

Question

Explanation:

Equate segment lengths using perpendicular bisector properties

Calculate the length of segment AD

Determine the length of segment DC

Answer: