Answer:
The fourth vertex must be located at [tex]Z(x,y) = (4, -1)[/tex]. The graph of the figure is included below.
Step-by-step explanation:
Let be [tex]X(x,y)[/tex], [tex]Y(x,y)[/tex], [tex]Z(x,y)[/tex] and [tex]W(x,y)[/tex] so that a rectangle is formed. Hence, we must satisfy the following conditions:
[tex]X(x,y) = (a, c)[/tex] (1)
[tex]Y(x,y) = (a, d)[/tex] (2)
[tex]Z(x,y) = (b, c)[/tex] (3)
[tex]W(x,y) = (b, d)[/tex] (4)
[tex]a < b[/tex] (5)
[tex]c < d[/tex] (6)
If we know that [tex]a = -1[/tex], [tex]b = 4[/tex], [tex]c = -1[/tex], [tex]d = 1[/tex], then we have the following points:
[tex]X(x,y) = (-1, -1)[/tex]
[tex]Y(x,y) = (-1, 1)[/tex]
[tex]Z(x,y) = (4, -1)[/tex]
[tex]W(x,y) = (4,1)[/tex]
Then, the fourth vertex must be located at [tex]Z(x,y) = (4, -1)[/tex].
