Transformations Flashcards

All 21 cards in this deck

What does the column vector $\begin{pmatrix} 3 \\ -2 \end{pmatrix}$ tell you about a translation?

Move 3 units right and 2 units down.
Top number = horizontal (right if positive), bottom number = vertical (up if positive).

What are the steps to translate a shape by a column vector?
e.g. translate by $\begin{pmatrix} 4 \\ -1 \end{pmatrix}$

1. Read the vector: 4 right, 1 down.
2. Move every vertex 4 right and 1 down.
3. Join the new vertices — the image is the same size and shape.

What must you state to fully describe a translation?

The word "translation" and the column vector.
e.g. translation by $\begin{pmatrix} 5 \\ -4 \end{pmatrix}$

Which properties of a shape are unchanged by a translation?

Lengths, angles and orientation are all unchanged — only the position changes.
The image is congruent to the object.

What must you state to fully describe a reflection?

The word "reflection" and the equation of the mirror line.
e.g. reflection in the line $y = 3$

What is the equation of the $x$-axis when it is used as a mirror line?

$y = 0$

What are the steps to reflect a shape in a given mirror line?
e.g. reflect in the line $y = 3$

1. Draw the mirror line $y = 3$.
2. Measure each vertex's perpendicular distance to the line, e.g. a vertex 2 above it.
3. Mark the image vertex the same distance on the other side (2 below) and join up.

Where does the mirror line $y = x$ lie on a coordinate grid?

A diagonal line through the origin sloping upwards at $45^\circ$, through all points whose $x$ and $y$ coordinates are equal.

True or false? A point that lies on the mirror line stays in the same place after a reflection.

True.
Its distance from the mirror line is zero, so the image point is on top of it.

True or false? A reflection keeps the orientation of the shape the same.

False.
The image is flipped (orientation reversed), though it is still congruent to the object.

What three things must you state to fully describe a rotation?

The angle, the direction (clockwise or anticlockwise) and the centre of rotation.
e.g. rotation $90^\circ$ clockwise about $(0, 0)$

True or false? A rotation of $180^\circ$ must have its direction stated.

False.
Clockwise and anticlockwise give the same image for $180^\circ$, so no direction is needed.

A rotation of $90^\circ$ anticlockwise is the same as which rotation clockwise?

$270^\circ$ clockwise.

What are the steps to rotate a shape about a given centre using tracing paper?
e.g. rotate $90^\circ$ anticlockwise about $(0, 0)$

1. Trace the shape and mark the centre $(0, 0)$.
2. Hold a pencil point on the centre and turn the paper a quarter turn anticlockwise.
3. Draw the shape in its new position and label it.

What single transformation is the same as a reflection in the $x$-axis followed by a reflection in the $y$-axis?

A rotation of $180^\circ$ about the origin $(0, 0)$.

True or false? A rotation changes the side lengths and angles of a shape.

False.
Lengths and angles are unchanged, so the image is congruent to the object.

What must you state to fully describe an enlargement?

The word "enlargement", the scale factor and the centre of enlargement.
e.g. enlargement, scale factor 2, centre $(0, 0)$

What are the steps to enlarge a shape by a scale factor from a given centre?
e.g. scale factor 2, centre $(0, 0)$

1. Count from the centre to a vertex, e.g. 3 right and 1 up.
2. Multiply by the scale factor: 6 right and 2 up — plot the image vertex.
3. Repeat for every vertex and join them up.

What happens to a shape when it is enlarged by scale factor $\frac{1}{2}$ from a centre?

The image is half the size, with each vertex's distance from the centre halved.

True or false? A scale factor of $\frac{1}{3}$ makes the shape smaller, so it is not called an enlargement.

False.
It is still an enlargement — scale factor $\frac{1}{3}$, and the image is three times smaller.

True or false? An enlargement by scale factor 3 makes all the angles 3 times bigger.

False.
Angles stay the same; only lengths are multiplied by 3, so the image is similar to the object.