Question

(04.02 mc)
segment ab falls on line ( 2x - 4y = 8 ). segment cd falls on line ( 4x + 2y = 8 ). what is true about segments ab and cd?

• they are perpendicular because they have the same slope of -2.
• they are perpendicular because they have slopes that are opposite reciprocals of -2 and ( \frac{1}{2} ).
• they are lines that lie exactly on top of one another because they have the same slope and the same y - intercept.
• they are lines that lie exactly on top of one another because they have the same slope and a different y - intercept.

Explanation:

Step1: Rewrite line AB in slope-intercept form

Start with $2x - 4y = 8$. Isolate $y$:
$-4y = -2x + 8$
$y = \frac{-2}{-4}x + \frac{8}{-4}$
$y = \frac{1}{2}x - 2$
Slope of AB: $m_1 = \frac{1}{2}$

Step2: Rewrite line CD in slope-intercept form

Start with $4x + 2y = 8$. Isolate $y$:
$2y = -4x + 8$
$y = \frac{-4}{2}x + \frac{8}{2}$
$y = -2x + 4$
Slope of CD: $m_2 = -2$

Step3: Check slope relationship

Multiply the slopes: $m_1 \times m_2 = \frac{1}{2} \times (-2) = -1$
Slopes are opposite reciprocals, so lines are perpendicular.

Answer:

They are perpendicular because they have slopes that are opposite reciprocals of -2 and $\frac{1}{2}$.