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Bezzdna [24]
3 years ago
7

3. Find the circumcenter of triangle EFG with E(2,6), F(2,4), and G(6,4)

Mathematics
1 answer:
Papessa [141]3 years ago
3 0

Answer:

(4,5)

Step-by-step explanation:

We are to find the circumcenter of triangle EFG with vertices

E(2,6), F(2,4), and G(6,4)

Let S(x,y) be the circum center.  Then this point is equidistance from E, F and

G

i.e. ES=FS=GS\\ES^2 =FS^2 =GS^2

(x-2)^2+(y-6)^2 =(x-2)^2+(y-4)^2 =(x-6)^2+(y-4)^2 \\i.e. x^2-4x+4+y^2-12y+36 = x^2-4x+4+y^2-8y+16 = x^2-12x+36+y^2-8y+16 \\4y = 20: y =5\\8x=32\\x=4

Thus circumcenter is (4,5)

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