multiple choice

b is the midpoint of ac. determine ab.

image showing a line segment ac with midpoint b. the length of ab is labeled as 6x - 4 and the length of bc is labeled as 4x + 26.

a. ab = 86
b. ab = 10
c. ab = 44
d. ab = 8

Question

multiple choice

b is the midpoint of ac. determine ab.

image showing a line segment ac with midpoint b. the length of ab is labeled as 6x - 4 and the length of bc is labeled as 4x + 26.

a. ab = 86
b. ab = 10
c. ab = 44
d. ab = 8

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Segment Midpoint Definition", "Geometric Segment Solving" ], "current_concepts": [ "Linear Equations", "Segment Midpoint Definition", "Geometric Segment Solving" ] } ## Set up the midpoint equation Using the *Linear Equations* knowledge point $$ \begin{aligned} AB &= BC \ 6x - 4 &= 4x + 26 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} 2x - 4 &= 26 \ 2x &= 30 \ x &= 15 \end{aligned} $$ ## Calculate the length of AB Using the *Linear Equations* knowledge point $$ \begin{aligned} AB &= 6(15) - 4 \ AB &= 90 - 4 \ AB &= 86 \end{aligned} $$

(A) $AB = 86$

(B) $AB = 10$

(C) $AB = 44$

(D) $AB = 8$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Segment Midpoint Definition" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set up the midpoint equation

Solve for x

Calculate the length of AB

Answer: