Question

15. Find the coordinates of the circumcenter of triangle ABC With the vertices A(3,-1) B(-3,-11) C(3,-8)

Answer 1

The coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

How to determine the coordinates?

In order to determine the coordinates of the circumcenter of triangle ABC with the given vertices, let its circumcenter be P(x, y). Thus, PA = PB = PC.

By squaring all sides of triangle ABC, we have:

PA² = PB² = PC²

From PA² = PB², we have:

(x - 3)² + (y - (-1))² = (x - (-3))² + (y - (-11))²

(x - 3)² + (y + 1)² = (x + 3)² + (y + 11)²

x² - 6x + 9 + y² + 2y + 1 = x² + 6x + 9 + y² + 22y + 121

-12x - 20y = 120

-3x - 5y = 30    ..........equation 1.

From PB² = PC², we have:

(x - (-3))² + (y - (-11))² = (x - 3)² + (y - (-8))²

(x + 3)² + (y + 11)² = (x - 3)² + (y + 8)²

x² + 6x + 9 + y² + 22y + 121 = x² - 6x + 9 + y² + 16y + 64

12x + 6y = -57     ..........equation 2.

Solving eqn. 1 and eqn. 2 simultaneously, we have:

x = -2.5 and y = -4.5.

Therefore, the coordinates of the circumcenter of triangle ABC with the given vertices are (-2.5, -4.5).

Read more on circumcenter here: brainly.com/question/11581885

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