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?

(a+b, c)

(b, a+c)

(2b, c)

(2a, c)

Answer 1

(a+b, c)

Explanation:

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Answer 2

(a+b, c)

Explanation:

The distance of the side along the x-axis is given by a-0 = a.

The length of the side opposite this must also be a units long; this means the x-coordinate of the fourth vertex will be at b+a, or a+b.

Since opposite sides are parallel and the top left vertex has a y-coordinate of c, the fourth vertex must have a y-coordinate of c.

This makes the coordinates of the fourth vertex (a+b, c).