Question

Please help!!! I need this!!

A triangle has vertices (0,0), (2,4), and (5,1). What are the coordinates of the circumcenter?, or the same triangle with vertices (0,0), (2,4), and (5,1), what are the coordinates of the orthocenter?

and could I have steps please?

Answer 1

The circumcenter of the triangle with vertices (0,0), (2,4), and (5,1) is located at (3,2).

To find the circumcenter, use the formula:

Cx = (x1 + x2 + x3)/3

Cy = (y1 + y2 + y3)/3

In this case, Cx = (0 + 2 + 5)/3 = 3

Cy = (0 + 4 + 1)/3 = 2

Therefore, the circumcenter of the triangle is located at (3,2).

The orthocenter of the triangle with vertices (0,0), (2,4), and (5,1) is located at (2.5, 2.5).

To find the orthocenter, use the following equation:

Hx = (x1 + x2 + x3)/3

Hy = (y1 + y2 + y3)/3

In this case, Hx = (0 + 2 + 5)/3 = 2.5

Hy = (0 + 4 + 1)/3 = 2.5

Therefore, the orthocenter of the triangle is located at (2.5, 2.5).

Explanation: