Question

In a coordinate proof involving a parallelogram, Vito places the parallelogram on the coordinate plane with one vertex at the origin and one side along the x-axis. The coordinates for the other vertices are given as follows: (0, 0), (2c, 0), (2a, 2b). What coordinates should he assign to the fourth vertex of the parallelogram?

a) \( (2c, 2b) \)
b) \( (2c + 2a, 2b) \)
c) \( (2a, 2c) \)
d) \( (2c + 2ab, 2a) \)

Answer 1

The coordinates for the fourth vertex of the parallelogram should be (2c, 2b).

Step-by-step explanation:

The given coordinates for the three vertices of the parallelogram are (0, 0), (2c, 0), and (2a, 2b). As one side of the parallelogram is along the x-axis, the fourth vertex must have the same y-coordinate as (2a, 2b), which is 2b. Therefore, the coordinates for the fourth vertex are (2c, 2b).