Question

find the circumcenter of angle ABC with vertices A( 1,1 ) B( 5,1 ) and C( 1,5 ) also include proofs on a graph.

Answer 1

(3,3)

Explanation:

Plot points A(1,1) B(5,1) and C(1,5) on the coordinate plane. These points determine right triangle with right angle at vertex A.

The circumcenter of right triangle ABC is the midpoint of the hypotenuse.

Find the midpoint of the hypotenuse:

`x_O=(5+1)/(2)=3\\ \\y_O=(1+5)/(2)=3`

Thus, the circumcenter has the coordinates O(3,3)