Question

What are the coordinates of the circumcenter of the triangle with vertices F(0,1), G(3,1), and H(3,5)?

Answer 1

ANSWER


`(1.5,3)`

Step-by-step explanation

The given triangle has vertices,

F(0,1), G(3,1), and H(3,5)

The coordinates of the circumcenter is the point of intersection of the perpendicular bisectors of any two sides of the given triangle.

Side FG has end points F(0,1) and G(3,1).

The y value is constant.

This means it is a horizontal line, therefore the perpendicular bisector is a vertical line that passes through the midpoint of F and G.

The midpoint is (1.5,1)

The perpendicular bisector is


`x = 1.5`

Side GH is also a vertical line because the x-value is constant.

The perpendicular bisector is a horizontal line that goes through the midpoint of G(3,1) and H(3,5).

The midpoint is (3,3)

The perpendicular bisector has equation,


`y = 3`

The two perpendicular bisectors will meet at,


`(1.5,3)`

These are the coordinates of the circumcenter.

See graph in attachment.