Question

David is writing a coordinate proof involving a parallelogram. Knowing that the opposite sides of a parallelogram are congruent, David places his parallelogram on the coordinate plane such that one vertex is at the origin and one side lies along the x-axis. What coordinates should he assign to the fourth vertex of the parallelogram?

1) (b, a + c)
2) (2b, c)
3) (a + b, c)
4) (2a, c)

Answer 1

The coordinates of the fourth vertex of the parallelogram are (B, 0).

Step-by-step explanation:

In a parallelogram, the opposite sides are congruent. If one vertex is at the origin and one side lies along the x-axis, the fourth vertex can be determined by applying this property. Since one side lies along the x-axis, the opposite side must also be parallel to the x-axis. This means that the y-coordinate of the fourth vertex will be the same as the y-coordinate of the first vertex, which is 0. The x-coordinate of the fourth vertex will be the same as the x-coordinate of the third vertex, which is B.

Therefore, the coordinates of the fourth vertex are (B, 0).