Question

1. Find the coordinates of the circumcenter for ∆DEF with coordinates D(1,1) E (7,1) and F(1,5). Show your work.




2. What is the length of the 2nd base of a trapezoid if the length of one base is 24 and the length of the midsegment is 19? Show your work.

Answer 1

1. Draw an accurate drawing of the triangle in the coordinate axis, as shown in the picture.

FD and DE are perpendicular, because D and F have the same x coordinate, and D and E the same y coordinate.

Let A(4, 1) be the midpoint of DE and B(1, 3) be the midpoint of FD.

Draw the perpendiculars from A and B. They meet at O(4, 3), since AO is parallel to DF and BO is parallel to DE.

the point where the perpendicular bisectors of the sides meet is the circumcenter, so the circumcenter is O(4, 3)


2. 

Let the length of the second base be x. 

the length of the midsegment is the sum of the ases divided by 2.

$19= \frac{x+24}{2}$

19*2=x+24

38=x+24

x=38-24=14


Answers:

1) O(4, 3)
2) length of second base = 14 units