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A reflection in math is when a shape is flipped over the x or y axis by counting how many units the points are away from the axis and putting the point on the other side the same distance away. Shapes which are reflections are labeled with a '. Example: Shape ABC was reflected over the x axis to create shape A'B'C'.
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Transform shapes by a combination of translation, reflection and rotation and know that area and angles are unchanged
In a transformation the shape does not change, only position, size and direction can change. That means, all the angles of the transformed shape do not change.
A combination of transformations just means doing more than one transformation to the same shape. For example, an enlargement and reflection means you enlarge the shape, then you reflect the enlarged shape.
How do you do transformations?
There are four transformations, which TERRy can help us remember: Translation Enlargement Rotation Reflection y
Translation
The position of the shape is moved up/down/sideways, but it does not change in size or direction.
Enlargement
This means increasing the size of a shape by a 'scale factor' from a particular point, which is called the centre of enlargement. Enlargement changes size and position but not direction.
If the shape is complicated to enlarge, take it step by step by taking the corners of the shape and 'enlarging' it one by one.
Enlarging a shape
We want to enlarge a shape with scale factor 3, with centre of enlargement (1,1)
Suppose we have an 'L' shape. Let's start with Corner A, which has coordinates (2,3).
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To get to A from the centre of enlargement, we have to go right 1 step and up 2 steps.
A scale factor of 3 means we multiply these distances by 3.
So now, to get to A' from the centre of enlargement, we have to go right 3 steps and up 6 steps.
These coordinates (4,7), because (1,1) is the centre of enlargement.
Finding the centre of enlargement
You can use a ruler to draw lines connecting each corner from the original shape to same corner in the enalrged shape. where all these points meet is the centre of enlargement.
Rotation
Every point on a rotated shape is at the same distance from the centre of rotation. It stays the same size, but changes in direction.
There are no tricks to finding the centre of rotation, it is done by observing, but remember every point must be at the same distance.
To rotate an object, again take each corner one by one and rotate it using a protractor. If the rotation is by 90o,180o,270^{o} then we you can use the grid on the paper.
For example, if you want to rotate the point (2,3) about the origin 90^{o} clockwise, insteading of going right 2 steps and up 3 steps, we go down 2 steps and right 3 steps, giving you the coordinates (3,2) (remember up and down give you ycoordinate, and left and right give you x coordinates, it doesn't matter what order it is in!)
Reflection
Reflection means we take the mirror image of a shape, where the mirror would be, we call it the line of symmetry. It stays the same, but changes in direction.
You can use tracing paper to help you get an idea of how to reflect a shape.
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