Investigation: Rearrange a room using transformations

Sometimes, we might feel the need for change or maybe we are adding a new piece of furniture, but we will rearrange a room. Some rooms will have lots of space, while others might be very tight for space.

We want to create a scale drawing of a room and then create a few different options for the set-up of the room.

Choose a room in your house or your school. On the blank piece of paper, do a rough sketch of the room.

Measure every length of the room using the measuring tape and put the measurements on your rough sketch. This does not need to be to scale, it is just to record the measurements.

Based on your measurements, create a scale drawing of this room on your first piece of grid paper. You can use your proportional reasoning to create find an appropriate scale factor based on the size of your room and the size of your paper. For example, 2 \text{ ft} = 1 \text { in}.

Measure at least four pieces of furniture or other large objects in the room and mark them down on your rough sketch.

Using your second piece of grid paper, cut out a scaled version of each piece of furniture.

Set up the room as it is currently set up using your cut-out pieces.

Create another set up for the room using only translations.

For each piece of furniture, state the transformations which have taken place.

Create another set up for the room using any kind of transformation.

For each piece of furniture, state the transformations which have taken place