Rotation about a Point in the Plane

object

square

triangle

letter L

translation by -p

(for reference only;sliders are inactive.)

horizontally (x axis)

0

vertically (y axis)

0

rotation (angle)

θ

0

translation by p

horizontally (x axis)

0

vertically (y axis)

0

θ

x1

1

y1

1

matrix of the rotation about p = (0, 0)

=

In this Demonstration you can rotate a square, a triangle, or the letter L about the point

p=(x,y)

in the plane, choosing the coordinates

(x,y)

with the "translation by

p

" sliders or by dragging the point in the graphic. Change the angle

θ

to see the rotation about the point

p

. The

3×3

matrix of the rotation is given by the product of three operations (from right to left): translation by

-p

, rotation around the origin, and translation back by

p

.