Question

Let G(u, u) = (u + u, u-v). For what value of m is the image of the line u horizontal line? mu + b a vertical line? A

Answer 1

$\begin{align*} G(u,v)&=G(u,mu+b)\\ &=(u+mu+b, u-(mu+b))\\ &=((1+m)u+b,(1-m)u-b) \end{align*}$

The image is vertical means the u coordinate is a constant, Which is possible when $(1+m)u=0$

That is $1+m=0$ , which gives $m=-1$

The image is Horizontal means the v coordinate is a constant, Which is possible when $(1-m)u=0$

That is $1-m=0$ , which gives $m=1$