BIG idea: Visualization

You can use visualization to find the image of a figure for a transformation.

Task 1

Each figure below is part of a capital letter in the English alphabet. To find the whole letter, combine the figure with its image for the appropriate rotation or reflection. What letter corresponds to each figure? What transformation produces each letter?

Image Long Description

BIG idea: Transformations

You can use transformations to describe a change in the position of a point.

Task 2

The arcs in the photo below appear to be paths of stars rotating about the North Star. To produce this effect, the photographer set a camera on a tripod and left the shutter open for an extended time. If the photographer left the shutter open for a full 24 hours, each arc would be a complete circle.

You can model a star's “rotation” in the coordinate plane. Place the North Star at the origin. Let P(1, 0) be the position of the star at the moment the camera's shutter opens. Suppose the shutter is left open for 2 h 40 min, with the arc ending at P ′ . p prime , .

1. What angle of rotation maps P onto P ′ ? p prime , question mark
2. What are the x- and y-coordinates of P ′ p prime  to the nearest thousandth?
3. What translation rule maps P onto P ′ ? p prime , question mark

BIG idea Coordinate Geometry

You can use coordinate geometry to prove a dilation image is similar to its preimage.

Task 3

Copy the graph below. On the same set of axes, graph the image of MNOP for a dilation with center (0, 0) and scale factor 2. Use coordinate geometry and the definition of similar polygons to prove that MNOP is similar to its image.