Question

The diagram shows a general parallelogram with a vertex at the origin and one side along the x-axis. What are the coordinates of D, the point of intersection of the diagonals of parallelogram ABCO? How do you know? (Step by step)

Answer 1

• D = (a + b, c)

Explanation:

The diagonals of the parallelogram bisect each-other.

Point D is the midpoint of AC or BD.

Use the midpoint equation to find the coordinates (x, y) of D:

• x = 1/2(2a + 2b) = a + b
• y = 1/2(2c + 0) = c
• D = (a + b, c)