When reflecting a 2-D shape remember that:
- the shape and its image are of opposite orientation
- a 2-D shape and its image are congruent
- there is an equal distance from the
mirror line to both the 2-D shape and its
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
Transformations - Reflection
Rules for performing a reflection across an axis When reflecting across the y-axis, the y-coordinates remain the same and the x-coordinates change to their opposites.
When reflecting across the y-axis, the x-coordinates remain the same and the y-coordinates change to their opposites.
Transformational Geometry - Reflection over a Diagonal
In this video we perform a reflection of a shape over a diagonal line of reflection. We do two examples, one where the shape overlaps the line of reflection.
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
When describing the
direction of rotation, we use the terms clockwise and
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
- all vertices move together 1/4
(180°) , or 3/4
(270°) of a turn
in the same direction, either clockwise or counter clockwise
- the shape and its resulting image are congruent
- the orientation of the shape and its image are different
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.
Rotations. 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.
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:
- the 2-D shape and its image are congruent
- the 2-D shape and its image have the same orientation (the vertices of
the translated image will be in the same relative position as the original
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:
- the shape and its image will have the same orientation
- all vertices move together
- each vertex moves the same way
If the translation is:
• to the left, the x- coordinate will decrease
• to the right, the x- coordinate will increase
• downward, the y- coordinate will decrease
• upward, the y- coordinate will increase
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.