math problem?

Question

1.V W is the median of a trapezoid that has the bases MN and
PO, with V on OM and W on PN. If the vertices of the trapezoid are M(2,6), N(4,6), P(10,0), and O(0,0) find the coordinates of V and W.






2.VW is the media of the trapezoid that has the bases MN and PO, with V on PM and W on ON. If four of the points are M(5,10), N(9,10), V(3,7), and W(11,7), find the coordinates of P and O.

Answer 1

1.V W is the median of a trapezoid that has the bases MN and
PO, with V on OM and W on PN. If the vertices of the trapezoid are M(2,6), N(4,6), P(10,0), and O(0,0) find the coordinates of V and W.

The coordinates of V are x=(2+0)/2=1 and y = (6+0)/2 = 3
The coordinates of W are x=(2+10)/2 =6 and y = (6+0)/2 =3

2.VW is the media of the trapezoid that has the bases MN and PO, with V on PM and W on ON. If four of the points are M(5,10), N(9,10), V(3,7), and W(11,7), find the coordinates of P and O.

The coordinates P and O are (x,y) and (x1,y1)
(x + 5)/2 = 3
x+5 = 6
x=1, (y+10)/2 = 7 so y+10 = 14 so y=4
So coordinates of P are (1,4)

(x1+9)/2 = 11
x1+9 = 22
x1 = 13, so coordinates of O are (13,4)

Answer 2

1) Make a sketch of the trapezoid so that you know the parallel sides -- in this case MN and OP. The median of a trapezoid connects the midpoints of the non-parallel sides, so we want the midpoints of sides MO and NP. Use the coordinates of the endpoints (2,6) and (0,0) and you should get (1,3) -- Add the "x" values and divide by 2 and add the "y" values and divide by 2. Now you try the midpoint for NP. That's right!!! (7,3).

This method should get you through the second problem as well.