Question

The points A(0,0), B(2,4), and D(7,0) are three of the four vertices of a parallelogram. What are the possible coordinates for the fourth vertex?

Answer 1

To find the coordinates of the fourth vertex of the parallelogram, subtract the coordinates of point A from point B to find the difference vector, and then add the difference vector to the coordinates of point D.

Step-by-step explanation:

The coordinates of the fourth vertex of the parallelogram can be determined by finding the difference vector between point B and point A, and then adding it to point D.

Given that A(0,0), B(2,4), and D(7,0), we subtract the coordinates of point A from point B to find the difference vector: B - A = (2 - 0, 4 - 0) = (2, 4).

Next, we add the difference vector to the coordinates of point D to obtain the coordinates of the fourth vertex: (7, 0) + (2, 4) = (9, 4).