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)
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)
Answers
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.
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.
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