# The vertices of the trapezoid are J(4m, 4n), K(4q, 4n), M(4p, 0), and L(0, 0). How do you find the midpoint of the midsegment of the trapezoid Midsegment=HN?

Jul 13, 2018

Mid point of the mid segment is (m+2p+q), 2n)

#### Explanation:

$J \left(4 m , 4 n\right) , K \left(4 q , 4 n\right) , L \left(0 , 0\right) , M \left(4 p , 0\right)$

H is the mid point of JK and N the mid point of LM

$H \left(x , y\right) = \frac{4 m + 4 q}{2} , \frac{4 n + 4 n}{2} = \left(\left(2 m + 2 q\right) , 4 n\right)$

$N \left(x , y\right) = \frac{4 p + 0}{2} , \frac{0 + 0}{2} = \left(2 p , 0\right)$

Mid point of HN O is

$O \left(x , y\right) = \left(\frac{2 m + 2 q + 4 p}{2} , \frac{4 n + 0}{2}\right)$

Mid point of the mid segment is (m+2p+q), 2n)