Question

I need help with geometry.

Answer 1

1.

In any trapezoid, the length of the midsegment is $\frac{|base_1|+|base_2|}{2}$

substituting the known values:

$\frac{24+|base_2|}{2}=19$

$24+|base_2|=38$

$|base_2|=38-24=14$

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:

$O=( \frac{1+7}{2} , \frac{5+1}{2} )=(4, 3)$


Answer:

1. 14

2. (4, 3)