Question

Connor is constructing rectangle ABCD. He has plotted A at (−2, 4), B at (0, 3), and C at (−2, −1). Which coordinate could be the location of point D?
D (−5, 1)
D (−4, 0)
D (−3, 11)
D (−2, 2)

Answer 1

Answer:

D (−4, 0)

Step-by-step explanation:

The image attached shows all given coordinates. There you can observe that point D must be placed at (-4, 0) to enclose a rectangle.

We can also demonstrate this by finding that sides AD and BC are congruent.

Side AD.

$d_{AD} =\sqrt{(0-4)^{2}+(-4-(-2))^{2} } =\sqrt{16+4}=\sqrt{20}$

Side BC.

$d_{BC}=\sqrt{(-1-3)^{2} +(-2-0)^{2} } =\sqrt{16+4}=\sqrt{20}$

As you can observe, sides AD and BC are congruent. Therefore, point D must be at (-4,0), to enclose a rectangle.