Find the circumcenter of triangle EFG with

Question

E(3,6), F(3,4), and G(7,4). please help :)

Answer 1

For EF, the midpoint is (3,5) and the slope would be -2/0. The perpendicular slope would be 0.

Plugging that in, you'd get:

5 = 0(3) + b

5 =  b


So, the equation for that bisector would be:

y = 5

For EG, the midpoint is (5,5) and the slope is -1/2. The slope of the perpendicular bisector is (2).

Plugging that in, we get:

5 = 2(5) + b

5 = 10 + b
-5 = b

The equation for that perpendicular bisector would therefore be:

y =2x- 5



y = 5
y =2x- 5
these equal and solving, we get:

5 = 2x-5

x=10/2=5

y=5

So, the intersection of the perpendicular bisectors is (5, 5).

Therefore ,circumcenter is (5, 5)