Answer:
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.
[tex]d_{AD} =\sqrt{(0-4)^{2}+(-4-(-2))^{2} } =\sqrt{16+4}=\sqrt{20}[/tex]
[tex]d_{BC}=\sqrt{(-1-3)^{2} +(-2-0)^{2} } =\sqrt{16+4}=\sqrt{20}[/tex]
As you can observe, sides AD and BC are congruent. Therefore, point D must be at (-4,0), to enclose a rectangle.
The coordinates of point D is (-4,0)
Rectangles have parallel and equal opposite sides, and all interior angles of the rectangles have a measure of 90 degrees
The coordinates are given as:
A = (-2,4)
B = (0,3)
C = (-2,1)
Start by calculating the distance AB
[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]AB = \sqrt{(-2 - 0)^2 + (4 - 3)^2}[/tex]
Calculate distance CD as follows:
[tex]CD = \sqrt{(x_2 - x_1)^2 + (y_2 -y_1)^2}[/tex]
So, we have:
[tex]CD = \sqrt{(x +2)^2 + (y +1)^2}[/tex]
The opposite sides are equal.
So, we have:
[tex]\sqrt{(x +2)^2 + (y +1)^2} = \sqrt{(-2 - 0)^2 + (4 - 3)^2}[/tex]
Square both sides
[tex](x +2)^2 + (y +1)^2 = (-2 - 0)^2 + (4 - 3)^2[/tex]
This gives
[tex](x +2)^2 + (y +1)^2 = (-2)^2 + (1)^2[/tex]
By comparison, we have:
[tex]x + 2 = -2[/tex]
[tex]y +1 = 1[/tex]
Solve for x and y
[tex]x=-4[/tex] and [tex]y = 0[/tex]
Hence, the coordinates of point D is (-4,0)
Read more about rectangles at:
https://brainly.com/question/6564657
