Question

4. AB formed by (-3, 8) and (2,3) CD formed by (-4, 6) and (-8, 2) perpendicular parallel or neither

Answer 1

We need to calculate the equation of the segment AB, First, we need to calculate the slope

(-3, 8) =(x1,y1)

(2,3) =(x2,y2)

`m=(y_2-y_1)/(x_2-x_1)=(3-8)/(2+3)=(-5)/(5)=-1`

the equation is

`\begin{gathered} y-8=-1(x+3) \\ y-8=-x-3 \\ y=-x-3+8 \\ y=-x+5 \end{gathered}`

then we will calculate the same for the segment CD

(-4, 6) =(x1.y1)

(-8, 2) =(x2,y1)

`m=(y_2-y_1)/(x_2-x_1)=(2-6)/(-8+4)=(-4)/(-4)=1`

the equation is

`\begin{gathered} y-6=1(x+4) \\ y-6=x+4 \\ y=x+4+6 \\ y=x+10 \end{gathered}`

with the slopes, we can notice

mAB=-1

mCd= 1

because the slopes are inverse between each other, we can assume the lines given are perpendicular