Answer:
Circumcenter of triangle [tex](4,-1)[/tex]
Step-by-step explanation:
Given coordinates are [tex](1,1)(1,-3)(7,-3)[/tex]
We will draw these points on the graph.
Let [tex]A(1,1)[/tex], [tex]B(1,-3)[/tex] and [tex]C(7,-3)[/tex]
We can see it is a right-angle triangle.
Let [tex]O[/tex] be the midpoint of line [tex]AC[/tex]
So, the coordinate of the point [tex]O[/tex] will be
[tex]A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=(\frac{1+7}{2},\frac{1+(-3)}{2})\\ \\O=(\frac{8}{2},\frac{-2}{2})\\\\O=(4,-1)[/tex]
Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.
So, coordinates of circumcenter is [tex](4,-1)[/tex]
