Find the coordinates of the circumcenter for ∆def with coordinates d(1,3) e (8,3) and f(1,-5). * show all work!

Let the coordinates of the circumcentre O of the triangle DEF be (x, y). Circumcentre of a triangle is equidistant from each of the vertices.

1. Distance OD=distance OE, then:

.

2. Distance OD=distance OE, then:

.

Solve the system:

,

,

.

Then

.

the coordinates of the circumcenter for ∆DEF are x=4.5, y=-1.

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