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)

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

So, we have:

Calculate distance CD as follows:

So, we have:

The opposite sides are equal.

So, we have:

Square both sides

This gives

By comparison, we have:

Solve for x and y

and

Hence, the coordinates of point D is (-4,0)

Read more about rectangles at:

link

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.

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

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)