In these lessons, Grade 6 students will learn about reflection, rotation and translation.
The following diagrams show the Transformations: Translation, Reflection and Rotation. Scroll down the page for examples and solutions.
When reflecting a 2-D shape remember that:
When reflecting a 2-D shape across a horizontal line of reflection, the x-coordinates of the vertices do not change, but the y-coordinates do change.
When reflecting a 2-D shape across a vertical line of reflection, the y-coordinates of the vertices do not change, but the x-coordinates do change.
When reflecting a 2-D shape across a diagonal line of reflection, both the x-coordinates and y-coordinates of the vertices change.
Transformations - Reflection
Rules for performing a reflection across an axis
Transformational Geometry - Reflection Over A Diagonal
In this video we perform a reflection of a shape over a diagonal line of reflection.
There are two examples, one where the shape overlaps the line of reflection.
When describing a rotation, we must include the amount of rotation, the direction of turn and the center of rotation.
Rotations can be described in terms of degrees (E.g., 90° turn and 180° turn) or fractions (E.g., 1/4 turn and 1/2 turn).
When describing the direction of rotation, we use the terms clockwise and counter clockwise.
In Grade 5, we rotated shapes about a vertex of that shape. In Grade 6, we will rotate about a centre of rotation on a vertex, outside the shape and within the shape.
When describing the positional change of the vertices of a given 2-D shape to the corresponding
vertices of its image as a result of a rotation, remember that
Using tracing paper we can trace the shape on the paper and place a dot on the point of rotation. Place the tip of a pencil on the point of rotation and turn tracing paper the indicated direction and amount for that particular rotation to see the position of the rotated image. We can then transfer the traced shape on the grid.
How To Rotate A Shape On A Coordinate Grid Using Tracing Paper?
In order to rotate a shape on a coordinate grid you will need to know the angle, the direction and the centre of rotation.
The angle could be 90 degrees (half turn), 180 degrees (1/2 turn) or 270 degrees ( ¾ turn). The direction can be clockwise or anticlockwise.
The centre of rotation is given as a coordinate and this is where you place your pencil on the tracing paper when you turn the shape around.
How to Performing a Rotation using Tracing Paper?
How to do a basic rotation using tracing paper.
This rotation used (0,0) as the rotation point and rotated 90° clockwise.
In a translation:
Remember to label the vertices of the shape (e.g. A, B, C, D) and the corresponding vertices of the reflected image (A', B', C', D'). A' is read as A prime.
When describing the positional change of the vertices of a given 2 D shape to the corresponding vertices of its image as a result of a translation, we need to keep in mind the following:
If the translation is:
In the transformation shown below:
We describe the translation as " Left 4 and Up 3"
The x-coordinates of the vertices decreased by 4.
The y-coordinates of the vertices increased by 3.
Transformations - Translating A Triangle On The Coordinate Plane
This tutorial reviews how to perform a translation on the coordinate plane using a triangle.
Transformational Geometry (Translations, Rotations, Reflections)
Translation, Reflection, Dilation, and Rotation
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