Question

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

Answer 1

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