Rotations in Geometry
ζ
Rotations
Dr Frost
Objectives:
Be able to rotate shapes about a given centre and by a
given angle, and to be able to describe the transformation when a
shape has been rotated.
The original shape
is known as the:
OBJECT
?
The shape after being
transformed is known as the:
IMAGE
?
The three things that describe a
rotation are:
1.
The centre of rotation.
2.
The angle
3.
The sense
(Clockwise or anticlockwise)
?
?
?
A rotation 90
°
anticlockwise
about the point (2,2).
Now describe this transformationin
your books!
A rotation 90
°
clockwise about the
point (-2, 1)
?
And this one!
A rotation of 180
°
about the point (4, 0)
?
And this one! (and now I’m being nasty –
I’ve hidden the centre of rotation
)
A rotation of 90
°
clockwise about the
point (0, 0), i.e. the
origin
.
?
We’re able to describe a rotation. But if we’re given the
description, we also need to be able to do the rotation!
That rotation was
misshapen and unsightly...
like your face.
Rotate the object 180
°
about the point (1,1).
When rotating by 180
°
, take each point (vertex) on the object, and imagine a construction
line to the centre of rotation. Continue this line using the same distance to get the
corresponding point on the image.
Not bad, but my dog has
more rotation skill than
you do.
Rotate the object 90
°
anticlockwise about the
point (2,2).
When rotating by 90
°
, again, take each point (vertex) on the object, and imagine a
construction line to the centre of rotation. But this time, imagine that line being rotated by
90
°
. Make sure you count your squares across the up/down.
I’ll tell you what... That
was one phenomenal
rotation performance.
Rotate the object 90
°
clockwise about the origin.
Learn how to rotate shapes around a center by a specified angle and describe the resulting transformation. Explore concepts like center of rotation, angle, and sense of rotation. Practice rotations with various examples and understand the process step by step.
Uploaded on Jul 18, 2024 | 2 Views
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Presentation Transcript
Dr Frost Rotations Objectives: Be able to rotate shapes about a given centre and by a given angle, and to be able to describe the transformation when a shape has been rotated.
8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 ROTATE Warning: Pressing this button may result in death or loss of limbs. REFLECT Warning: Pressing this button may result in bowel problems. TRANSLATE Warning: Do not press if you are pregnant or suffer from a heart condition. ENLARGE Warning: Pressing this button may result in loss of girlfriend. -6
8 The three things that describe a rotation are: 6 ? ? 1. The centre of rotation. 2. The angle 3. The sense (Clockwise or anticlockwise) The original shape is known as the: OBJECT? ? 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 The shape after being transformed is known as the: IMAGE ? -4 Click to DESCRIBE TRANSFORMATION A rotation 90 anticlockwise about the point (2,2). Click to ROTATE -6
8 Now describe this transformationin your books! 6 A rotation 90 clockwise about the point (-2, 1) ? 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Click to ROTATE -6
8 And this one! A rotation of 180 about the point (4, 0) ? 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Click to ROTATE -6
8 And this one! (and now I m being nasty I ve hidden the centre of rotation ) 6 A rotation of 90 clockwise about the point (0, 0), i.e. the origin. ? 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Click to ROTATE -6
8 We re able to describe a rotation. But if we re given the description, we also need to be able to do the rotation! 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 -6
8 When rotating by 180 , take each point (vertex) on the object, and imagine a construction line to the centre of rotation. Continue this line using the same distance to get the corresponding point on the image. 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Rotate the object 180 about the point (1,1). That rotation was misshapen and unsightly... like your face. -6
8 When rotating by 90 , again, take each point (vertex) on the object, and imagine a construction line to the centre of rotation. But this time, imagine that line being rotated by 90 . Make sure you count your squares across the up/down. 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 Not bad, but my dog has more rotation skill than you do. anticlockwise about the point (2,2). Rotate the object 90 -6
8 6 4 2 -10 -8 -6 -4 -2 2 4 6 8 10 -2 -4 I ll tell you what... That was one phenomenal rotation performance. clockwise about the origin. Rotate the object 90 -6
