Question

select whether \\( \overleftrightarrow{ab} \\) and \\( \overleftrightarrow{cd} \\) are parallel, perpendicular, or neither. graph each line on a separate sheet of paper to verify your answer.\\( a(4, -2) \\), \\( b(-2, -8) \\), \\( c(4, 6) \\), \\( d(8, 5) \\)\
select choice

Explanation:

Step1: Calculate slope of $\overrightarrow{AB}$

Given points \( A(4, -2) \) and \( B(-2, -8) \), the slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
So, \( m_{AB} = \frac{-8 - (-2)}{-2 - 4} = \frac{-6}{-6} = 1 \).

Step2: Calculate slope of $\overrightarrow{CD}$

Given points \( C(4, 6) \) and \( D(8, 5) \), using the slope formula:
\( m_{CD} = \frac{5 - 6}{8 - 4} = \frac{-1}{4} = -\frac{1}{4} \).

Step3: Compare slopes

For parallel lines, slopes are equal (\( m_1 = m_2 \)); for perpendicular lines, slopes are negative reciprocals (\( m_1 \times m_2 = -1 \)).
Here, \( m_{AB} = 1 \) and \( m_{CD} = -\frac{1}{4} \). Since \( 1
eq -\frac{1}{4} \) (not parallel) and \( 1 \times (-\frac{1}{4}) = -\frac{1}{4}
eq -1 \) (not perpendicular), the vectors are neither parallel nor perpendicular.

Answer:

Neither