Finally, we can measure the distance from the preimage to the line of reflection. We will also locate the image at the same distance from the given line on the opposite side of the line of reflection.
As we can see, the x-coordinate of the image is the same as the x-coordinate of the preimage, which is a. Let's find the y-coordinate. To do this, we will add the distance between the x-axis and the line of reflection, which is 6, and the distance between the line of reflection and the image, which is b + 6.
6 + b + 6 = 12 + b
Notice that the reflected point lies on the negative side of the y-axis. Therefore, to obtain its y-coordinate, we should put a minus sign before the distance we found.
-(12 + b) ⇔ - 12 - b
We found that ( a, - 12 - b) is the image of the point (a,b) after a reflection across the line y = - 6. This corresponds to option D.
