Question

On the coordinate plane shown, the points A(4, 4), B(−2, 4), and C(−2, −3)

are plotted. What will be the coordinates of point D if ABCD forms a square?

A graph is shown in the xy-plane. The values on the x-axis ranges from negative 8 to 8 in increments of 2 and the values on the y-axis ranges from negative 8 to 8 in increments of 2. Three points Upper A, Upper B, and Upper C are marked on the graph. The point Upper A is 4 units above the x-axis and 4 units to the right of the y-axis. The point Upper B is 4 units above the x-axis and 2 units to the left of the y-axis. The point Upper C is 3 units below the x-axis and 2 units to the left of the y-axis.

A.

(4,−3)

B.

(−4,−3)

C.

(3,−4)

D.

(4,−2)

Answer 1

To form a square, the length of each side will be the same. Therefore, the distance between points A and B must be equal to the distance between points B and C.

The distance between points A and B can be found using the distance formula:

√[(4 - (-2))^2 + (4 - 4)^2] = √36 = 6

The distance between points B and C can also be found using the distance formula:

√[(-2 - (-2))^2 + (-3 - 4)^2] = √49 = 7

Since these distances are not equal, we cannot form a square with these three points. Therefore, the answer is none of the above.