Maths: Grade 7 Space and Shape: Transformation Geometry
TRANSFORMATION GEOMETRY A transformation means changing the position of a shape without chang...
Maths: Grade 7 Space and Shape: Transformation Geometry
TRANSFORMATION GEOMETRY A transformation means changing the position of a shape without changing its size or form. It is a way of moving a shape. Examples of geometric transformations are reflection, rotation and translation. These transformations produce congruent figures, that is, shapes exactly the same size. Congruent shapes have the exact same lengths and the exact same size angles. So a congruent shape is one that is identical in shape and size. A shape can be congruent, even if it has been transformed. Example
So in transformation geometry we look at how shapes can be changed.
Translation This is also called a slide. To slide or translate a shape, you move it along in any direction, i.e., up or down, to the left or right, or diagonally without turning it or making it bigger or smaller. The shape just slides into a new position. When a shape is translated, every part of the shape moves in the same distance and in the same direction with the size of the shape staying the same.
Maths: Grade 7 Space and Shape: Transformation Geometry
Go to the link below to see examples of slides / translations: https://mycyberwall.co.za/get-smart/maths/grade-6/transformations You will see from these examples that the shapes have not changed, just moved position.
Reflection This is also called a flip. To flip a shape is to reflect it over a line. Reflection is a mirror image of the original shape. The reflected shape is called the image and the size of the reflected shape stays the same. The image or reflection is the reverse of the original shape.
Example
Pattern
Reverse Image of Pattern
We can reflect a shape to the left or right. Example
Maths: Grade 7 Space and Shape: Transformation Geometry
Go to the link below to see examples of flips / reflections: https://mycyberwall.co.za/get-smart/maths/grade-6/transformations You will see from these examples that the shapes look different because they have been flipped over.
Rotation This is also called a turn. To rotate a shape means to move or turn a shape around a point. The point is called the centre of rotation. For example, if you place your pen on a piece of paper, you can turn the paper around and keep the pen in the same position. You are rotating the paper around the centre point. This is the same as a turn. Rotation changes the position of the shape but the size of the shape stays the same. Rotation can occur in a clockwise or anti-clockwise direction.
To describe a rotation, it is important to note the position of the centre of rotation, state the angle of rotation and indicate the direction of rotation. Example
Shape P has been rotated 180o clockwise around the centre of rotation.
Maths: Grade 7 Space and Shape: Transformation Geometry
Click on the link below to see examples of turns through 90o, 180o, 270o and 360o. https://mycyberwall.co.za/get-smart/maths/grade-6/transformations You will see from the examples that you can turn the shape a quarter rotation (90o), a half rotation (180o), a three quarter rotation (270o) or a full rotation (360o).
Symmetry A shape is symmetrical if it can be folded in half with the one half being exactly the same as the other half. We call the fold, the line of symmetry or axis of symmetry. It can also be an angled or slanted line. A line of symmetry is sometimes called a mirror line and symmetry is often called a mirror image. Some shapes have many lines of symmetry. Some have only one and lots of shapes are not symmetrical at all. We call shapes that are not exactly the same when folded in half asymmetrical. Examples
Three lines of symmetry
No lines of symmetry
Enlargements and Reductions When we make a shape bigger, it is called an enlargement and when we make a shape smaller it is called a reduction. Enlargements and reductions change the size of figures by increasing or decreasing the length of sides, but keeping the angles the same, producing similar rather than congruent figures.
Maths: Grade 7 Space and Shape: Transformation Geometry
Similar shapes look the same but are different in size. They have the same size angles but the length of the sides is in proportion. We do enlargements and reductions according to a scale factor.
Example Shape A and Shape B below have the same angles but their lengths and widths have changed.
Shape A:
Shape B:
Length
=
4
Length
=
12
(4 x 3 = 12)
Width
=
2
Width
=
6
(2 x 3 = 6)
We can see that Shape A is three times smaller than Shape B and Shape B is three times the size of Shape A. Therefore the scale factor is 3.
![Transformation]](https://kipdf.com/img/300x300/transformation_5ab545e51723dd349c8189ea.jpg)
