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

Answer:

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

Step-by-step 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 $Z(x,y) = (4, -1)$.