Name: Laura

Who is asking: Student
Level: Secondary

Question:
Given: A (1,2) B (9,-2) C (7,2) D (3,4)

Find the endpoints of the median. Use exact values. Write the equation using the letters from the given trapezoid. Verify the theorem using algebra.

I tried using the distance formula to find lines AB and CD but didnt not come out with a perfect square. Is this right?

Thanks,
Laura

I didn't get a perfect square either. This doesn't surprise me. I wouldn't expect the length of a side of a trapezoid to be an integer, even if the verticies have integer coordinates.

I think there are two points here.

1. To construct the median of a trapezoid you join the midpoints of two parallel sides.
   
   
2. The midpoint of a line segment from (a,b) to (c,d) has coordinates ( ^a+c/₂, ^b+d/₂). That is the coordinates of the midpoint are the averages of the coordinates of the endpoints.