Question

ANOTHER BIG QUESTION, 100 POINTS

Write reciprocals, opposites, the same, or negative reciprocals in each blank.

The slopes of parallel lines are _.

The slopes of perpendicular lines are _.

Find the slopes of lines AB and CD. Show your work.

Line AB goes through points A(3, 4) and B(7, 7).

Line CD goes through points C(0, 0) and D(-6, 8).

Use Parts I and II to determine if AB and CD are parallel, perpendicular, or neither. Explain your answer.
Graph and on the grid to support your answer from Part III.

Answer 1

Answer:

The slopes of parallel lines are the same

The slopes of perpendicular lines are negative reciprocals

Line AB

$\textsf{let}\:(x_1,y_1)=(3,4)$

$\textsf{let}\:(x_2,y_2)=(7,7)$

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{7-4}{7-3}=\dfrac{3}{4}$

Line CD

$\textsf{let}\:(x_1,y_1)=(0,0)$

$\textsf{let}\:(x_2,y_2)=(-6,8)$

$\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{8-0}{-6-0}=-\dfrac{4}{3}$

As the slopes of AB and CD are negative reciprocals of each other, lines AB and CD are perpendicular.