Line AB is on the coordinate plane and does not pass through the origin. Line AB is dilated with a scale factor of 3 and a center of dilation at the origin to create line A′B′.
Does that mean that AB would be like A(2,2) B(4,4) and when dilated, it becomes Aprime(6,6)Bprime(12,12) ? 3 times bigger and the primes are far away from the non primes? Correct?
No, your understanding is not correct.
If line AB does not pass through the origin, the center of dilation at the origin means that the origin (0,0) is the fixed point around which the dilation occurs.
To find the coordinates of A′ and B′ after dilation with a scale factor of 3, you would multiply the coordinates of A and B by 3.
For example, if A(2,2) and B(4,4), the new coordinates after dilation would be A′(6,6) and B′(12,12).
The coordinates become 3 times larger, but they are not "far away" from the original coordinates. They simply move along the same line, keeping the same slope and direction, but with a greater distance from the origin.