Find the circumcenter of a triangle with vertices o(0, 0), v(0, 26), and w(−10,0).

Circumcenter is .

Step-by-step explanation:

Given:

The three vertices of triangle OVW are .

Circumcenter is a point inside the triangle which is equidistant from each of the vertices of the triangle.

Let be the circumcenter.

Distance between two points and  is given as:

So, as per the definition of circumcenter, distance of point from point is equal to distance of point from point .

So, OC = VC

or

.

Similarly, distance of point from point is equal to distance of point from point .

or

.

Therefore, the circumcenter of the triangle with the given vertices is .

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.