Question

Points W and X are on Wx. Y and Z are on YZ. Are WX and YZ parallel, perpendicular, Or neither?W(1, 3) X(2, 6)Y(4,4) Z(7,3)

Answer 1

Firstly, we need to find the equation of the line passing through the points

W(1, 3) and X(2, 6)

and also the equation of the line passing through the points Y(4, 4), and Z(7, 3)

The line WX is given as

`\begin{gathered} (y-3)/(x-1)=(6-3)/(2-1) \\ \\ \Rightarrow(y-3)/(x-1)=3 \\ \\ \Rightarrow y-3=3x-3 \\ \\ \Rightarrow y=3x \end{gathered}`

The line YZ is given as

`\begin{gathered} (y-4)/(x-4)=(3-4)/(7-4) \\ \\ \Rightarrow(y-4)/(x-4)=-(1)/(3) \\ \\ \Rightarrow y-4=-(1)/(3)(x-4) \\ \\ \Rightarrow y-4=-(1)/(3)x+(4)/(3) \\ \\ \Rightarrow y=-(1)/(3)x+(4)/(3)+3 \\ \\ \Rightarrow y=-(1)/(3)x+(13)/(3) \end{gathered}`

The gradient of WX is 3

The gradient of YZ is -1/3

Since the product of the gradient WX and YZ

`3*-(1)/(3)=-1`

Hence WX is perpendicular to YZ