Question

The art club is designing a rectangular mural for the school hallway. Three corners are located at (-1, -1), (-1, 1), and (4, 1) on teh coordinate plane. What would be the forth vertex on the coordinate plane below?

Answer 1

The fourth vertex must be located at
`Z(x,y) = (4, -1)`. The graph of the figure is included below.

Explanation:

Let be
`X(x,y)`,
`Y(x,y)`,
`Z(x,y)` and
`W(x,y)` so that a rectangle is formed. Hence, we must satisfy the following conditions:

`X(x,y) = (a, c)` (1)

`Y(x,y) = (a, d)` (2)

`Z(x,y) = (b, c)` (3)

`W(x,y) = (b, d)` (4)

`a < b` (5)

`c < d` (6)

If we know that
`a = -1`,
`b = 4`,
`c = -1`,
`d = 1`, then we have the following points:

`X(x,y) = (-1, -1)`

`Y(x,y) = (-1, 1)`

`Z(x,y) = (4, -1)`

`W(x,y) = (4,1)`

Then, the fourth vertex must be located at
`Z(x,y) = (4, -1)`.