Question

What are the coordinates of the circumcenter of a triangle with vertices a(0,1), b(2, 1), and c(2, 5)? enter your answer in the boxes. (, ).

Answer 1

The coordinate of the circumcenter of a triangle is (1,3).

Here we have to find the coordinates of the circumcenter of a triangle.

Given data:

The vertices of the triangle are:

A = (0,1)

B = ( 2,1)

C= ( 2,5)

The formula to find the distance between the two points:

Distance = $\sqrt{(x2 - x1)^{2} + (y2-y1)^{2} }$

In the same manner distance between AB, BC, and AC are:

AB = $\sqrt{(2-0)^{2} + (1-1)^{2} }$

    = 2

BC = $\sqrt{(2-2)^{2} + (5-1)^{2} }$

      = 4

AC = $\sqrt{(2-0)^{2} + (5-1)^{2} }$

     = 2√5

So by the Pythagoras, we get to know that the triangle is a right-angle triangle.

The circumcenter of a right-angle triangle is the midpoint of the hypotenuse.

Midpoint of AC = (0+2)/2 , (1+5)/2

                         = 2/2, 6/2

                         = 1,3

Therefore the coordinate of the circumcenter is (1,3).

To know more about the circumcenter refer to the link given below:

brainly.com/question/21299234

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