Find the circumcenter of the triangle ABC.

A ( - 4,3), B (5,7), C (-4,7).

Circumcenter O (0.5, 5)

Step-by-step explanation:

Circumcenter O (x, y)

OA = OB = OC

OA² = (x + 4) ² + (y - 3) ²

OB² = (x - 5) ² + (y - 7) ²

OC² = (x + 4) ² + (y - 7) ²

OA² = OC² : (x + 4) ² + (y - 3) ² = (x + 4) ² + (y - 7) ²

(y - 3) ² = (y - 7) ² y² - 6y + 9 = y² - 14y + 49

8y = 40

y = 5

OB² = OC² : (x - 5) ² + (y - 7) ² = (x + 4) ² + (y - 7) ²

x² - 10x + 25 = x² + 8x + 16

18x = 9

x = 0.5

Circumcenter O (0.5, 5)