Performing a rotation to match figures

Use one rotation to map quadrilateral ABCD to the other quadrilateral. So to map this one to this one right over here, use a number between 0 and 360° to describe the angle. Counterclockwise is positive, so you're going to want to move it counterclockwise to try to get it to map there.

The only option they give us because they want us to do it with one rotation is the rotation tool. We have to think about where—what do we want to rotate around? What point? If we put it right over here, it looks like this point, point A, does correspond to this point right over here.

So, if we were to rotate this around—not 90, but it looks like 180°—around this point, point A would show up over here. It feels like point… Let's see, is that right? Is that right? Or, well, let's actually just try it out. Point A would show up over… No, no, no, that's not right. That doesn't seem to… Let's try it out, because if we rotated 180°... Oh, actually, I was right! It did match up.

That's why this is interesting; it tests your visualization skills. So it did actually match up, and what I did is I put that point of rotation exactly between those points, because it looked like 180° around this point. So, rotation by 180° about (1, -1). The center of rotation is (1, -1), and the angle of rotation is 180°.

Point A maps to this point right over here, so point A maps to the point (1, -1). And point C, which is diagonally opposite point A, maps to this point right over here, which is (6, -6).

We got it right!