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

Question

can you please explain how i can find this answer? i am having trouble

Answer 1

this might be a good place to start:

https://brilliant.org/wiki/triangles-circumcenter/

You can also work out where the perpendicular bisectors of two of the sides meet.

Answer 2

the circumcenter is equidistant from all three vertices

it lies on the intersection of the three perpendicular bisectors of the sides

midpoint DF is ... (1,3) ... b DF is ... y = 3

midpoint DE is ... (4,1) ... b DF is ... x = 4

Answer 3

steve
i got -2a + 1 - 2b+1 = 14a+28 + 2b+1 i dont know what to do after
and
14a + 28 - 8b-16 + 2a + 1 - 10b+20 but i dont know what to do after this one too :/

Answer 4

what, you forgot your Algebra I ?

-2a + 1 - 2b+1 = 14a+28 + 2b+1
14a + 28 - 8b-16 = 2a + 1 - 10b+20

kinda messy, so simplify a bit

16a+4b = -27
12a+2b = 9

Now you can use those to solve for a and b, which I assume are the coordinates of the circumcenter.

Answer 5

are we all solving the same problem?

Answer 6

I didnt forget i just have trouble understanding as quick and easy as others im not good in math...
but thankyou for helping me.