The coordinates of parallelogram UVWZ are U(a, 0), W(c - a, b), and Z(c, 0). Find the coordinates of V without using any new variables.1. (c,b)2. (a,b)3. (0,b)4. (b,0)

check the picture below.

so, as you can see, the UV segment is parallel to ZW, and therefore, they're the same slope, hmmm wait just a second, what is the slope of ZW anyway?

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &Z&(~ c &,& 0~) % (c,d) &W&(~ c-a &,& b~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{b-0}{(c-a)-c}\implies \cfrac{b}{-a}[/tex]

since now we know the ZW slope, we also know what is the slope for UV, thus,

[tex]\bf \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &U&(~ a &,& 0~) % (c,d) &V&(~ x &,& y~) \end{array} \\\\\\ % slope = m slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{y-0}{x-a}~~=~~\stackrel{ZW's~slope}{\cfrac{b}{-a}} \\\\\\ \begin{cases} y-0=b\implies \boxed{y=b}\\ -----------\\ x-a=-a\implies \boxed{x=0} \end{cases}\qquad \qquad V~(0,b)[/tex]