Question

Are AB and CD parallel, perpendicular, or neither?*
1. A(-4, 8), B(4, 10), C(1, 1), D(-2, 13)

Answer 1

Answer:

Perpendicular

Step-by-step explanation:

Given

$A = (-4, 8)$

$B = (4, 10)$

$C = (1, 1)$

$D = (-2, 13)$

Required

Is AB and CD parallel?

First, we need to calculate the slope (m) of AB and CD

$m = \frac{y_2 - y_1}{x_2 - x_1}$

For AB:

$A (x_1,y_1)= (-4, 8)$

$B(x_2,y_2) = (4, 10)$

So:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{10 - 8}{4 - (-4)}$

$m = \frac{10 - 8}{4 +4}$

$m = \frac{2}{8}$

$m = \frac{1}{4}$

For CD:

$C(x_1,y_1) = (1, 1)$

$D(x_2,y_2) = (-2, 13)$

So:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{13 - 1}{-2 - 1}$

$m = \frac{12}{-3}$

$m = -4$

For Lines to be parallel, the slope must be equal:

i.e. $m_1 = m_2$

This condition is not true because:

$\frac{1}{4} \neq -4$

For Lines to be perpendicular, the slope must be:

$m_1 = -\frac{1}{m_2}$

This implies:

$\frac{1}{4} = -\frac{1}{-4}$

$\frac{1}{4} = \frac{-1}{-4}$

$\frac{1}{4} = \frac{1}{4}$

Hence, the lines are perpendicular