1.
In any trapezoid, the length of the midsegment is [tex] \frac{|base_1|+|base_2|}{2} [/tex]
substituting the known values:
[tex] \frac{24+|base_2|}{2}=19 [/tex]
[tex]24+|base_2|=38[/tex]
[tex]|base_2|=38-24=14[/tex]
2.
Notice that since D and have the same y-coordinate, then DE is horizontal, and since F and D have the same x-coordinate, FD is vertical.
Thus FD and DE are perpendicular, so the triangle FED is a right triangle.
The median drawn from the right angle, is equal to half the hypotenuse.
That is, |DO|=1/2 |FE|, thus |OE|=|OF|=|OD|, are all radii of the circle centered at O.
O is the midpoint of EF, and is found by the Midpoint formula:
[tex]O=( \frac{1+7}{2} , \frac{5+1}{2} )=(4, 3)[/tex]
Answer:
1. 14
2. (4, 3)
