Question

The vertices of the trapezoid are the origin along with A(4p, 4q), B(4r, 4q), and C(4s, 0). Find the midpoint of the midsegment of the trapezoid

Answer 1

The midpoint of the midsegment of the trapezoid is (p+r+s,2q).

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.

`Midpoint=((x_1+x_2)/(2),(y_1+y_2)/(2))`

Midpoint of OA is

`P=((0+4p)/(2),(0+4q)/(2))=(2p,2q)`

Midpoint of BC is

`Q=((4r+4s)/(2),(4q+0)/(2))=(2r+2s,2q)`

Midpoint of the midsegment of the trapezoid is the midpoint of P and Q. So, the midpoint of PQ is

`M=((2p+2r+2s)/(2),(2q+2q)/(2))=(p+r+s,2q)`

Therefore, the midpoint of the midsegment of the trapezoid is (p+r+s,2q).