There are four main ways to mathematically alter a shape: translation, rotation, reflection and enlargement.
Translating a shape means to move its position while keeping the orientation and size of the shape intact. Translations are described using column vectors (xy), which means to move the shape x spaces to the right and y spaces up.
The square ABCD was originally in the top-right quadrant. It was then transformed to the bottom-left quadrant as shown below. Describe the transformation that took place.
The size and orientation of the shape is unchanged, so the shape has been translated.
To find the corresponding column vector, focus on one vertex and see where it moved to.
A=(1,1) gets mapped to A=(−4,−4).
The corresponding column vector is therefore (−5−5) as A moved 5 steps to the left and 5 steps down to end up at (−4,−4).
The transformation is a translation by column vector (−5−5).
Rotating a shape has three details associated with it:
The centre of rotation is the point you rotate everything around.
Describe the transformation that maps the shape ABCD to the shape A′B′C′D′ in the diagram below.
This is a rotation of 180° with centre O.
Note: In this case, there was no need to specify direction as a rotation of 180∘ clockwise is the same as a rotation of 180