code class="asciimath">Do as indicated. Show your complete solution. \Omega _(\gamma )\Omega _(\beta )\Omega _(\alpha )=(\Omega _(\alpha )\Omega _(\beta )\Omega _(\gamma ))^(-1)(\tau _(v)\Omega _(l))^(-1)=\Omega _(l)\tau _(-v) Show that the products of two distinct half-turs is a translation along the line joining their centers. If H_(1),H_(2) and H_(3) are half turns, prove that H_(1)H_(2)H_(3)=H_(3)H_(2)H_(1). Let P be any point. Prove that the half turn about P is given by H_(P)(x)=-x+2P for all xinE^(2). Let l=P+[v] be a line. Let m=Q+[v]. Show that if |v|=1, then \Omega _(l)\Omega _(m)=\tau _(w), where w= and \Omega _(m)\Omega _(l)=\tau _(-w).