ABCD is a trapezoid with
. P and Q are the midpoints of
respectively. The length of PQ is equal to __________.
Solution:Use the midpoint formula to find the coordinates of P and Q.
Coordinates of P: ( , ) = (, )
Coordinates of Q: ( , ) = ( + , )
Use the distance formula, = to find the lengths of AB, DC and PQ.
AB = = = 2
DC = = = (2 - 2)
PQ = = = ( + - )
|AB - DC| = |2 - (2 - 2)| = |2 - 2 + 2 |
= 2| + - |= 2PQ
So, PQ = |AB - DC|
Correct answer : (3)