Question

What are the coordinates of the circumcenter of the triangle ?

Answer 1

A=(-1,3)

B=(5,3)

C=(5,-5)

Explanation:

Answer 2

The answer to your question is (2, -1)

Explanation:

1.- Find half points

AB

Between A and B there are 6 units, then the half point is three units from point A to the right

(2, 3)

BC

Between B and C there are 8 units, then the half point is four units below the point B.

(5, -1)

AC

Xm = -1 + 5 / 2 = 4 / 2 = 2

Ym = 3 - 5 / 2 = - 2 / 2 = - 1

(2, -1)

2.- Find the equations of the mediatrices

AB

x = 2 because the line must be perpendicuar to AB

BC

y = - 1 because the line must be perpendicular to BC

AC

slope m =
`(-5 - 3)/(5 + 1)`

m =
`(-8)/(6)`

m =
`(-4)/(3)`

mediatrix AC

y + 1 = -4/3 (x -2)

3y + 3 = -4x + 8

4x + 3y = 8 - 3

4x + 3y = 5

3.- Find the circumcenter

When x = 2

4(2) + 3y = 5

8 + 3y =5

3y = 5 - 8

3y = -3

y = -3/3

y = -1

When y = -1

4x + 3(-1) = 5

4x - 3 = 5

4x = 5 + 3

4x = 8

x = 8/4

x = 2

Circumcenter (2, -1)