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lesya692 [45]
3 years ago
15

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

Mathematics
1 answer:
ohaa [14]3 years ago
6 0

Answer:

Perpendicular

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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}

<em>Hence, the lines are perpendicular</em>

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