Question

Consider the line segments AB and BC graphed on the coordinate plane shown. What will be the coordinates of point D if ABCD forms a parallelogram?

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 with coordinates (negative 4, negative 3), (negative 4, 7), and (3, 4) respectively. A line is formed by joining the points Upper A and Upper B and a line is formed by joining the points Upper B and Upper C.

A.

(3,−3)

B.

(3,0)

C.

(3,−4)

D.

(3,−6)

Answer 1

Since AB and BC are two sides of a parallelogram, their slopes must be the same:

slope of AB = (7 - (-3))/(-4 - (-4)) = 5
slope of BC = (4 - 7)/(3 - (-4)) = -3/7

Since these slopes are not equal, ABCD cannot be a parallelogram. Therefore, the question is invalid and there is no answer.