What does it mean to rotate about a line?
A solid of revolution is a three-dimensional figure obtained by rotating a two-dimensional figure (or curve) around a straight line (called the axis) that lies in the same plane. An example of a rotation about a line is the concept of a revolving door.
How do you rotate a circle around a point?
Informally: To rotate a shape, move each point on the shape the given number of degrees around a circle centered on the point of rotation. Make sure each new point is the same distance from the point of rotation as the corresponding original point.
What does it mean to rotate about a point?
To rotate a shape or object means to spin it around a specific point (center), without moving it in any other way. Rotation does not affect size or shape.
What happens to a line as it rotates?
You cannot move the line because you cannot move the points from which it is made of. Instead your rotated line is a completely new line which (as we say) looks like the former line, but “rotated”. The rotated line may be made from other points than the former one.
What is the formula for rotating about a point?
Rotation Formula
| Type of Rotation | A point on the Image | A point on the Image after Rotation |
|---|---|---|
| Rotation of 90° (Clockwise) | (x, y) | (y, -x) |
| Rotation of 90° (Counter Clockwise) | (x, y) | (-y, x) |
| Rotation of 180° (Both Clockwise and Counterclockwise) | (x, y) | (-x, -y) |
| Rotation of 270° (Clockwise) | (x, y) | (-y, x) |
What is the rule for rotating 90 degrees clockwise?
Here are the rotation rules: 90° clockwise rotation: (x,y) becomes (y,-x) 90° counterclockwise rotation: (x,y) becomes (-y,x) 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)