Question

Mathematics Tutorial: Rotating a shape around a point that isn't the Origin.

Answer 1

Our shape has the Coordinates below:
A (2,5)
B (4.3)
C (2,2)

Answer 2

We are rotating the shape around point C (2,2)

Answer 3

To make this easier, we are going to translate the shape, so that point C is on the Origin.

Answer 4

Point C is at (2,2) so we need to move it down 2 and left 2, do this with the other points too.

Answer 5

Our new shape Coordinates:
A (0,3)
B (2,1)
C (0,0)

Answer 6

We're going to rotate this ship 180 degrees around the Origin (Point C)

Answer 7

When you are rotating a shape 180 degrees the signs change, but the numbers don't. So our new Coordinates are:
A (0,-3)
B (2,1)
C (0,0)

Answer 8

Now we have rotated our shape.

Answer 9

Now we have to undo the translation by adding 2 to our x and y Coordinates.

Answer 10

Moving up 2 and right 2

Answer 11

So our final Coordinates are:
A (2,-1)
B (0,1)
C (2,2)

Answer 12

Here's a demo of what we did.

Answer 13

Original Shape w/ Coordinates:

Answer 14

Translating C to the Origin, as well as affecting the other points too.

Answer 15

Rotating 180 degrees:

Answer 16

Undoing the Translation:

Answer 17

That's how you rotate a shape around a point that is not the Origin!

Answer 18

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