Find the Intersection Using the Midpoint

Given that 0 has coordinates (0,0), move the points N to (6,0), M to (7,4), and L to (1,4) in the graph above.Move the line segments above the parallelogram using their points to draw and . (Remember they were called the "diagonals" of a parallelogram.) Move point P to their intersection. What do you get as its coordinates? Write the coordinate values in a pair (e.g., "(2,3).")

Back to our diagram: How will you use the Parallelogram Diagonals Theorem to find the coordinates of the intersection? By the Parallelogram Diagonals Theorem, the diagonals of a parallelogram bisect each other. So, the coordinates of the intersection are the (fill-in-the-blank) of diagonals and .

In the applet above, recall the values of the coordinates of the points O and M. Designate them as (x₁,y₁) and (x₂,y₂). I already did it for O: O = (x₁,y₁) = (0,0) M = (x₂,y₂) = (fill-in-the-blank)

Finally, using the Midpoint Formula, find the midpoint of O and M.

Does the midpoint you found in Step 4 match where you placed the point P in the applet above? Why or why not?