Performing a rotation to match figures

2m read

·Nov 11, 2024

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!

Khan Stories: Brooke Hogan

Smart Fish | Wicked Tuna

View All

Policy and the branches of government | AP US Government and Politics | Khan Academy

As we’ve discussed in other videos, the federal bureaucracy is a huge part of the US government, sometimes even called the fourth branch. It has more than two million employees who work in various agencies dedicated to implementing the law. So, the bureau…

Critically looking at data on ROC and economic growth over millenia | Macroeconomics | Khan Academy

So we’ve already talked about the general idea: the thesis that if the return on capital is greater than the growth of an economy, that could lead to inequality. Although we showed a case where, depending on the circumstances with the right numbers, that’…

Verifying inverse functions from tables | Precalculus | Khan Academy

We’re told the following tables give all of the input-output pairs for the functions s and t. So we see this first table here, we have some x’s, and then they tell us what the corresponding s of x is. Then, in this table, we have some x’s, and they tell u…

Limits by rationalizing | Limits and continuity | AP Calculus AB | Khan Academy

Let’s see if we can find the limit as x approaches negative one of ( \frac{x + 1}{\sqrt{x + 5} - 2} ). So our first reaction might just be, okay, well let’s just use our limit properties a little bit. This is going to be the same thing as the limit as x …

Anxious | Vocabulary | Khan Academy

Oh boy, oh geez, wordsmiths, I’m not feeling so hot about this word. I tell you what. The word is anxious, or if you prefer, anxious. It’s an adjective that means very worried. You might have seen it in its noun form, anxiety, which is the state of being …

"You Will NEVER Be Able to Afford to Retire" - BlackRock CEO Larry Fink

People working longer should we making a possible facility? Should we frankly increase the age for Social Security? What if I told you there was a $14 trillion crisis brewing in the United States that, until now, virtually no one had been paying attention…

Performing a rotation to match figures

More Articles