Flashcards · Maths · Transformations and Similarity
Reflections and Translations
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What is a transformation?
A change in the position, and sometimes the size, of a shape.
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What is the object and what is the image?
The object is the original shape and the image is the shape after the transformation.
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What stays the same in a reflection?
The size and shape, so the image is congruent to the object.
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How far is an image point from the mirror line?
The same distance as the object point, on the other side.
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How do you describe a reflection fully?
Say "reflection" and give the equation of the mirror line.
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What is the equation of the \(x\)-axis?
\(y = 0\).
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What is the equation of the \(y\)-axis?
\(x = 0\).
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What happens to the coordinates of a point reflected in the line \(y = x\)?
They swap.
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What happens to the coordinates of a point reflected in the line \(y = -x\)?
They swap and both change sign.
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What does a translation do?
Slides every point the same distance in the same direction.
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What does the top number of a column vector show?
The move to the right, or to the left if negative.
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What does the bottom number of a column vector show?
The move up, or down if negative.
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How do you find a translation from a point and its image?
Subtract the object coordinates from the image coordinates.
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Does a translation change the orientation of a shape?
No, the shape faces the same way.
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Does a reflection change the orientation of a shape?
Yes, it gives a mirror image.
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What should you write for "describe the transformation"?
The name of the transformation and all of its details.