Rotation Rules: Everything you Need to Know

What are the Rules for Rotation in Math? Here’s everything you need to know.

 

Read the brief Rotation in Math Definition including 90 Degree Rotation

 

What is the Definition of Rotation in Math Practice

Watch the video where we complete our Rotations Worksheet

Watch our free video on how to solve Rotations. This video shows how to solve problems that are on our free Rotation Rules worksheet that you can get by submitting your email above.

Watch the free Rotations video on YouTube here: Rotation Rules

Video Transcript:

This video is about rotation rules for math. You can get the worksheet used in this video for free by clicking on the link in the description below.

When we are talking about rotation rules what we are talking about are ways that we can spin a figure or a point, typically around the origin, which is the center of the graph. Figures can be rotated one of two ways. They can be rotated clockwise. Clockwise refers to the way the hand spins on a clock. If you look at a clock, the hand spins this way. That’s the direction you would be rotating or spinning the object on the coordinate grid. The figure can also rotate counterclockwise. Counterclockwise refers to the opposite direction of clockwise, or in this case the opposite way that the hands move on a clock. These are the two ways you can rotate a figure on the coordinate grid.

Just to give you a very easy example. If we had a here and we wanted to rotate it clockwise. It would rotate this way and it would become a prime down here. This would be a 90-degree rotation clockwise. You could also take a and rotate it counterclockwise which would go in this direction, and then a prime would be over here.

Another rotation rule is that you have to know that the degree measures of rotation are all in 90 degrees. If we rotate one quadrant either clockwise or counter clockwise that would be a 90 degree rotation. If we rotate it again it would be 90 more degrees or total from this point to this point would be 90 plus 90 or 180 degrees total. In this case we’re going clockwise and then if we went 90 more degrees, or if we want one more quadrant, it would be 90 more degrees and then total it would be 90 plus 90 plus 90 or 270 degrees total rotation.

You can do the same thing in the opposite direction. The same rotation rules would apply when going in the counterclockwise direction. If we go this way, it’s still 90 and then if we go one more quadrant it’s 90 more again, and then 180 total. Our next quadrant would be 90 more degrees and then 270 degrees total, and then of course if you went back to the original spot it would be 360 degrees or a full rotation around the origin.

The next rotation rule has to do with the quadrants. The quadrants are labeled in a counterclockwise rotation around the origin. This is quadrant one, quadrant two, quadrant three, and finally quadrant four. Every single coordinate in quadrant one will have a positive x value and a positive Y value, every single coordinate in quadrant two will have a negative x value and a positive Y value, quadrant three every single coordinate is negative negative, and then quadrant four every single coordinate is positive x and a negative Y. This is important to know because as you rotate around the origin and you end up in a different quadrant, the coordinates on your point will always match the coordinates of the quadrant.

So in this case our coordinate is to two our x value will be negative because we’re in the second quadrant and the y value will be positive. So it’s negative two, positive two.

The last rotation rule that you must know is that every time you rotate 90 degrees in either direction clockwise or counter clockwise you flip-flop the x and the y value. If we start here at 1, 2 and we rotate 90 degrees into quadrant four, the one and the two will become two one. Then our coordinate has to match that of the quadrant, which in this case is positive negative. The two is positive and the y is negative and then you can plot your new point. It’s two negative one and then if we wanted to rotate again one will become one two. It would rotate back but this time everything in this quadrant is negative negative so this would be negative one and this would be negative two and you’d plot it here. And then if you rotate it again the X and the y would flip-flop again, from one to two to one and then everything in quadrant two has a negative x value. Our point would be right there.

Number two on our rotation rules for math worksheet tells us to rotate figure ABCD 90 degrees counterclockwise. Here is figure ABCD, we have to rotate it 90 degrees counterclockwise. Counterclockwise is in this direction so it spins counter to the way the hands of a clock spin. We’re going to go 90 degrees and everything in this quadrant has a negative x value and a positive Y value.

Now we know that every time we rotate 90 degrees we have to flip-flop the X in the Y coordinates so  in this case we’re going 90 degrees counterclockwise. Our 3, 4 will become 4, 3 but we have to check to see what quadrant we are in. We’re in quadrant 2, which we already know is negative, positive. So all of our coordinates have to match our quadrant. In this case the quadrant is negative positive.

The x value has to be negative and the y value has to be positive. In order to get B Prime we have to flip-flop our X and our Y. Because we’re going 90 degrees rotation in this case it’s six, six. Everything in quadrant two has a negative x value and a positive Y value for coordinates. For C, our point is 9, 4. That has to be flip-flopped into 4, 9. Everything has to have a negative x value so that’s going to be a negative 4 and a positive 9. Finally our last coordinate is d, which is 6. It will become two, six because we have to flip-flop x and y and then the two is negative.

The last step is to graph our new figure. Here are the coordinates of our new vertices that we need to plot for our new figure. A prime is negative 4, 3 so we’ll graph that and we’ll also label it. B prime is negative 6, 6 and we will also label B prime. C prime is negative 4, 9 and finally D prime is negative 2, 6. Now we’ve graphed our new figure you can see that our figure has been rotated 90 degrees counterclockwise. This is going to be the solution for our second problem on our rotation rules worksheet.