How to find the Centre of Rotation

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And welcome to the maths doctor in this video. Were looking at how to to find the center of rotation. Theres a worksheet and solutions to accompany this at my website.
If youre watching from youtube. Ive provided a link below the video so here you can see i have triangle abc. I can rotate a full 360 degrees as youll see positive rotation gays anti clockwise.
But as you can see there is no visible centre of rotation and thats deliberate because were going to find it now im going to show you how to do a really really cool trick to find the center of rotation and im going to cheat because im going to use this fantastic package geogebra to do it for me. However im then going to go to a second example and use all the conventional maths tools and show you the proper way of doing. It with a compass and a ruler.
So this is how you do it firstly connect any two corresponding vertices at a and a dash and find the perpendicular bisector of that line or between those two points. So you can see this green line is the perpendicular bisector of a and a dash.

how to find the centre of rotation-0
how to find the centre of rotation-0

Now all you need to do is exactly the same between just one other pair of vertices. So lets say b and b. Find the perpendicular bisector of that line and where the two perpendicular bisectors.
Meet is the center of rotation. So lets put a little dot in there to indicate where that center of rotation is say as a coordinate that is seven across and one up. And its really quite nice as you rotate the shape of full 360 degrees.
You can see that the perpendicular bisectors remain intersected at that same point now of course. I could have joined the vertices c. And c.
Dash up as well and find the perpendicular bisector of those might as well do that now and now we have three perpendicular bisectors. All intersecting at that same point 7 1.

how to find the centre of rotation-1
how to find the centre of rotation-1

Which is the center of rotation. Now this will always work for any rotated object throughout any angle. So its a very powerful.
Very nice trick so lets have a look at doing one ourself. Without the software. So this time.
We have a rectangle abcd and heres a rotation of it in fact we can see i think its 140 degrees. Its been rotated. But that doesnt matter what im going to do is thats just a bit a little bit more accurate.
Im going to connect a and a and lets do lets say b b. I could do any two and now i have this fantastic compass tool.

how to find the centre of rotation-2
how to find the centre of rotation-2

And im going to lets just reflect that over im going to find the perpendicular bisector of a and e. So just as long as my compass span is past halfway. I can draw arc down there and one up here move the points to the other vertex.
Another arc. So my two arcs intersect ok very happy with that one and now were going to connect those two points up thatll be our first perpendicular bisector love it so we know that the centre of enlargement sorry its center of rotation is on that line somewhere so were going to do exactly the same this time on the line bibi say as long as my compass is past halfway. I can draw an arc and run up here oops lets be dark there and do the same from the other vertex there and here fantastic.
So we dont need the compass anymore. But we do now need to draw a straight line between that point. And that point now as you can clearly see the two perpendicular bisectors intersect at a different color at that point there four across one up that is indeed our centre of rotation for one say.
Thats a pretty cool technique okay so it will always work and i think what you really need is just a bit of practice and you can practice using my worksheet. Which can be found on the website. There are some solutions as well so if you found this video of value you can show your appreciation by clicking the donate link from my website and donate any amount you feel reflects the help that youve received okay thank you very much have fun and see you soon.
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how to find the centre of rotation-3
how to find the centre of rotation-3

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