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? responses (a b, c) begin ordered pair a plus b comma c end ordered pair (2a, c) begin ordered pair 2 a comma c end ordered pair (2b, c) begin ordered pair 2 b comma c end ordered pair (b, a c)

Answer 1

The fourth vertex coordinates for a parallelogram placed in a coordinate system with one vertex at the origin and one side along the x-axis should be (a + b, c), ensuring that the opposite sides remain congruent and parallel.

Step-by-step explanation:

When David is writing a coordinate proof involving a parallelogram and places one vertex at the origin with one side lying along the x-axis, assigning coordinates to the fourth vertex depends on the location of the other two vertices (not mentioned in the question).

However, one can deduce that the fourth vertex should be placed in such a way that the opposite sides of the parallelogram remain congruent and parallel.

Assuming we have vertices at (0,0), (a,0), and (b,c), we place the fourth vertex in a way that retains the properties of a parallelogram.

Since the opposite sides are congruent and parallel, the x-coordinate of the fourth vertex will match the x-coordinate of the opposite vertex (a) translated by the x-distance between the origin and the other known vertex (b), which is (a + b).

The y-coordinate will match the other non-origin vertex (c), resulting in the fourth vertex having coordinates (a + b, c).

Therefore, the correct coordinates for the fourth vertex in a parallelogram, given one vertex at the origin and one side along the x-axis, should be (a + b, c).