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

Explanation:

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<reasoning>

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
\[

$$\begin{aligned} AB &= 6(15) - 4 \\ AB &= 90 - 4 \\ AB &= 86 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(AB = 86\)</mcq-correct>
<mcq-option>(B) \(AB = 10\)</mcq-option>
<mcq-option>(C) \(AB = 44\)</mcq-option>
<mcq-option>(D) \(AB = 8\)</mcq-option>
</answer>

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Answer:

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<reasoning>

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
\[

$$\begin{aligned} AB &= 6(15) - 4 \\ AB &= 90 - 4 \\ AB &= 86 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(AB = 86\)</mcq-correct>
<mcq-option>(B) \(AB = 10\)</mcq-option>
<mcq-option>(C) \(AB = 44\)</mcq-option>
<mcq-option>(D) \(AB = 8\)</mcq-option>
</answer>

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