Question

identify the perpendicular lines from the following.

\\(4y = 2 + 4x\\) and \\(2y = 5 + 2x\\)

\\(4y = 2 + 4x\\) and \\(2y = 5 - 2x\\)

Explanation:

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<reasoning>

Find the slopes of the first pair of lines

\[

$$\begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\\ 2y &= 5 + 2x \implies y = x + \frac{5}{2} \implies m_2 = 1 \end{aligned}$$

\]

Find the slopes of the second pair of lines

\[

$$\begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\\ 2y &= 5 - 2x \implies y = -x + \frac{5}{2} \implies m_2 = -1 \end{aligned}$$

\]

Check the perpendicular condition

\[
m_1 \cdot m_2 = 1 \cdot (-1) = -1
\]
</reasoning>

<answer>
<mcq-option>(A) \(4y = 2 + 4x\) and \(2y = 5 + 2x\)</mcq-option>
<mcq-correct>(B) \(4y = 2 + 4x\) and \(2y = 5 - 2x\)</mcq-correct>
</answer>

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Answer:

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<reasoning>

Find the slopes of the first pair of lines

\[

$$\begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\\ 2y &= 5 + 2x \implies y = x + \frac{5}{2} \implies m_2 = 1 \end{aligned}$$

\]

Find the slopes of the second pair of lines

\[

$$\begin{aligned} 4y &= 2 + 4x \implies y = x + \frac{1}{2} \implies m_1 = 1\\ 2y &= 5 - 2x \implies y = -x + \frac{5}{2} \implies m_2 = -1 \end{aligned}$$

\]

Check the perpendicular condition

\[
m_1 \cdot m_2 = 1 \cdot (-1) = -1
\]
</reasoning>

<answer>
<mcq-option>(A) \(4y = 2 + 4x\) and \(2y = 5 + 2x\)</mcq-option>
<mcq-correct>(B) \(4y = 2 + 4x\) and \(2y = 5 - 2x\)</mcq-correct>
</answer>

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