Circle O is centered at the origin and has a radius of 5.

Circle O' is the image of circle O after a translation of T1,2. What is the center of circle O'? What is the radius of circle O'?

To find the center of circle O' after the translation, we need to apply the translation vector T1,2 to the center of circle O.

Since circle O is centered at the origin (0, 0), we apply the translation vector T1,2 to the origin. T1,2 represents a translation of 1 unit to the right (positive x-direction) and 2 units upwards (positive y-direction).

To find the new x-coordinate of the center of circle O', we add 1 to the x-coordinate of the origin:
New x-coordinate = 0 + 1 = 1

To find the new y-coordinate of the center of circle O', we add 2 to the y-coordinate of the origin:
New y-coordinate = 0 + 2 = 2

Therefore, the center of circle O' is (1, 2).

The radius of circle O' remains the same as the radius of circle O, which is 5. Translations do not affect the size of the shape, only its position. So, the radius of circle O' is also 5.