Question

find the coordinates of the circumcenter of triangle DEF
D(2,3)E(8,3)F(8,-1)

Answer 1

@Michele_Laino

Answer 2

here, we have to write the equations of at least two of the axes of two sides of such triangle

Answer 3

ok how do i do that

Answer 4

first step:
we have to write the equation of the side ED
please look at this drawing:

Answer 5

ok how would we write an equation though

Answer 6

now, the mid point of DE is located at \(x=5\) right?

Answer 7

I meant \(x=5,\;y=3\)

Answer 8

yes

Answer 9

so the axis of DE passes at that point and it is orthogonal with respect to DE. Suc axis has the subsequent equation:
\(x=3\), am I right?

Answer 10

such*

Answer 11

what is orthogonal?

Answer 12

I meant that the axis of DE has to be perpendicular to the segment DE

Answer 13

yes it would have to be

Answer 14

now, in a similar way, the axis of EF has to be perpendicular to EF, and it has to pass at midpoint of EF, and such midpoint is located at \((8,1)\) right?

Answer 15

yes it would

Answer 16

So, what is the equation of the axis of EF?