Question

Question #ef5bd

Answer 1

`(-1,-1)`

Explanation:

Hmm...

These coordinates seem to have a special relationships.

I have graphed them here:

Hey, these form a right triangle!

A circle that circumscribes a right triangles always has the hypotenuse of the right triangle as its diameter.

In our case, it looks like this:

Now, since the hypotenuse forms when we connect the points `(-4,1)` and `(2,-3)`, the center of the point is right between them.

This is obvious using the fact that the center of a circle is at the middle of the diameter.

We now find the midpoint between the points `(-4,1)` and `(2,-3)`.

The midpoint is: `((-4+2)/2,(1+(-3))/2)`

=>`((-2)/2,(-2)/2)`

`=>(-1,-1)`