TransformationsEdexcel IGCSE Maths: Flashcards

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What three pieces of information fully describe a rotation?

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What three pieces of information fully describe a rotation?: Centre of rotation, angle of rotation, and direction (clockwise/anticlockwise) — direction can be omitted for $180°$ .
What single piece of information (plus 'reflection') fully describes a reflection?: The equation of the mirror line, e.g. $x = 2$ or $y = x$ .
How do you fully describe a translation?: With a column vector $\begin{pmatrix} x \\\\ y \end{pmatrix}$ , giving horizontal then vertical movement.
What two pieces of information fully describe an enlargement?: The centre of enlargement and the scale factor $k$ .
Rule for reflecting $(a,b)$ in the line $y = x$ ?: Swap the coordinates: image is $(b,a)$ .
Rule for reflecting $(a,b)$ in the line $y = -x$ ?: Swap and negate both coordinates: image is $(-b,-a)$ .
Rule for rotating $(a,b)$ by $90°$ clockwise about the origin?: Image is $(b,-a)$ .
Rule for rotating $(a,b)$ by $90°$ anticlockwise about the origin?: Image is $(-b,a)$ .
What happens to a shape's area under an enlargement of scale factor $k$ ?: The area is multiplied by $k^2$ (side lengths are multiplied by $k$ ).
What is special about an enlargement with a negative scale factor?: The image is resized AND flipped through the centre, landing on the opposite side of the centre from the object, inverted.
Does a fractional scale factor (e.g. $k = \tfrac{1}{2}$ ) make the shape bigger or smaller?: Smaller — but it is still called an 'enlargement' in maths terminology.
Which of the four transformations always produces a congruent image (for $k \neq \pm1$ enlargements excluded)?: Translation, reflection, and rotation are always congruent to the object; enlargement is not (unless $k = \pm 1$ ).
Which transformation reverses orientation, making a mirror image?: Reflection.
How do you rotate a point about a centre that isn't the origin?: Subtract the centre's coordinates from the point, apply the origin rotation rule, then add the centre's coordinates back on.
How do you find the image of a point under enlargement from a centre?: Find the vector from the centre to the point, multiply it by the scale factor $k$ , then add it back to the centre.