207k views
4 votes
Segment AB has coordinates A(5, 6) and B(2, 2). Segment CD has coordinates C(-4,-9) and D(-8,2). Determine if AB and CD are parallel, perpendicular, or neither. justify your answer

User Cpinamtz
by
7.9k points

1 Answer

0 votes

the lines are not parallel,and the lines are not perpendicular

Step-by-step explanation

Step 1

find the slopes

when you have two points of a line P1 and P2 you can find the slope using


\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{where} \\ P1(x_1,y_1) \\ P2(x_2,y_2) \end{gathered}

for segment AB

P1(5,6)

P2(2,2)

replace


\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope1}=(2-6)/(2-5)=(-4)/(-3)=(4)/(3) \end{gathered}

for segment CD

P1(-4,-9)

P2(-8,2)


\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ \text{slope}=(2-(-9))/(-8-(-4))=(2+9)/(-8+4)=(11)/(-4)=(-11)/(4) \end{gathered}

Step 2

compare the slopes


\begin{gathered} \text{if slope1=slope2, then the lines are parallel} \\ \text{if slope1}\cdot slope2=-1,\text{ then, the lines are perpendicular} \\ \text{replacing} \\ \text{slope}1\cdot\text{slope}2=(4)/(3)\cdot(-11)/(4)=(-11)/(3) \end{gathered}

Hence, the lines are not parallel,and the lines are not perpendicular.

I hope this helps you

User Francesco Papagno
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories