Notes Transformations: Rotations



Notes Transformations: Rotations

Let’s take a look at some real life application of rotations:

|A _________ is a transformation that turns a figure about a fixed point |[pic] |

|called the __________________.  Rays drawn from the center of rotation to a | |

|point and its image form an angle called the _______________. An object and | |

|its rotation are the _______________________, but the figures may be | |

|_____________________ | |

|__________________________________.   | |

|Rotations are ______________! | |

Some practices of what rotations look like:



A (2,3) B (3,-2) C (–2,1)

|90 Clockwise |90 Counterclockwise |

|Coordinates of Pre- Image |Coordinates of Pre- Image |

|Coordinates of the Image (after Rotation) |Coordinates of the Image (after Rotation) |

| | |

|A(2,3) |A (2,3) |

| | |

| | |

|B (3,-2) |B (3,-2) |

| | |

| | |

|C (-2,1) |C (-2,1) |

| | |

| | |

| | |

|180 Clockwise |180 Counterclockwise |

|Coordinates of Pre- Image |Coordinates of Pre- Image |

|Coordinates of the Image (after Rotation) |Coordinates of the Image (after Rotation) |

| | |

|A (2,3) |A (2,3) |

| | |

| | |

|B (3,-2) |B (3,-2) |

| | |

| | |

|C (-2,1) |C (-2,1) |

| | |

| | |

| | |

|270 Clockwise |270 Counterclockwise |

|Coordinates of Pre- Image |Coordinates of Pre- Image |

|Coordinates of the Image (after Rotation) |Coordinates of the Image (after Rotation) |

| | |

|A (2,3) |A(2,3) |

| | |

| | |

|B (3,-2) |B (3,-2) |

| | |

| | |

|C (-2,1) |C (-2,1) |

| | |

| | |

| | |

|360 Clockwise |360 Counterclockwise |

|Coordinates of Pre- Image |Coordinates of Pre- Image |

|Coordinates of the Image (after Rotation) |Coordinates of the Image (after Rotation) |

| | |

|A (2,3) |A(2,3) |

| | |

| | |

|B (3,-2) |B (3,-2) |

| | |

| | |

|C (-2,1) |C (-2,1) |

| | |

| | |

See if you could come up with the rules for rotation!

|Degrees of Rotation |Clockwise Rule |Counterclockwise Rule |

|90 | | |

| | | |

|180 | | |

| | | |

|270 | | |

| | | |

|360 | | |

| | | |

Ex. 1) Draw the rotation of [pic] under a rotation of 90°

counterclockwise about the origin.

Give the coordinates of [pic].

Ex. 2) Draw the rotation of [pic] under a rotation of 180°

about the origin.

Give the coordinates of [pic].

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