Question

Circumcenter of triangle with coordinates of (1,1) (1,-3) (7,-3)

Answer 1

Circumcenter of triangle
`(4,-1)`

Explanation:

Given coordinates are
`(1,1)(1,-3)(7,-3)`

We will draw these points on the graph.

Let
`A(1,1)`,
`B(1,-3)` and
`C(7,-3)`

We can see it is a right-angle triangle.

Let
`O` be the midpoint of line
`AC`

So, the coordinate of the point
`O` will be

`A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=((1+7)/(2),(1+(-3))/(2))\\ \\O=((8)/(2),(-2)/(2))\\\\O=(4,-1)`

Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.

So, coordinates of circumcenter is
`(4,-1)`