Respuesta :
Answer:
The midpoint of the midsegment of the trapezoid is (p+r+s,2q).
Step-by-step explanation:
The vertices of the trapezoid are O(0,0), A(4p,4q), B(4r,4q) and C(4s,0).
If a line connects the midpoints of the two nonparallel sides of the trapezoid then it is known as midsegment of a trapezoid.
OC and AB are horizontal lines because the y-coordinated of their end points are same.It means OC and AB are parallel sides. So, we can say that OA and BC are non parallel sides.
[tex]Midpoint=(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})[/tex]
Midpoint of OA is
[tex]P=(\dfrac{0+4p}{2},\dfrac{0+4q}{2})=(2p,2q)[/tex]
Midpoint of BC is
[tex]Q=(\dfrac{4r+4s}{2},\dfrac{4q+0}{2})=(2r+2s,2q)[/tex]
Midpoint of the midsegment of the trapezoid is the midpoint of P and Q. So, the midpoint of PQ is
[tex]M=(\dfrac{2p+2r+2s}{2},\dfrac{2q+2q}{2})=(p+r+s,2q)[/tex]
Therefore, the midpoint of the midsegment of the trapezoid is (p+r+s,2q).
