# G.GCO.4 Exploring Rotations Around a Point not the Origin

Topic:
Rotation

## DIRECTIONS:

In the GeoGebra applet below: Use the slider tool to rotate Daffy Duck 90 degrees. After doing all this, please answer the question that appear below the applet.

## 1.

Let C = (2,-2) be the point about which points A and B (and Daffy Duck) are rotated. Place point A at (2, 3) and point B at (5, 1). When Daffy was rotated 90 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (x, y) of the image of B?

## Steps to Rotate an object 90 degrees counter-clockwise around (2, -2)

1) Translate (2, -2) to the origin by the vector <-2, 2>. 2) Translate each pre-image point by the vector <-2, 2>. 3) A(2, 3) = A'(0, 5) and B(5, 1) = B'(3, 3). 4) Rotate A' and B' 90 degrees counter-clockwise. 5) A"(-5, 0) and B"(-3, 3). 6) Fixed the center or rotation by undoing the vector of <-2, 2> by using the vector <2, -2>. 7) A'''(-3, -2) and B'''(-1, 1).

## 2.

Let C = (2,-2) be the point about which points A and B (and Daffy Duck) are rotated. Place point A at (2, 3) and point B at (5, 1). When Daffy was rotated 180 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (x, y) of the image of B?

## 3.

Let C = (2,-2) be the point about which points A and B (and Daffy Duck) are rotated. Place point A at (2, 3) and point B at (5, 1). When Daffy was rotated 270 degrees: What are the coordinates (x, y) of the image of A? What are the coordinates (x, y) of the image of B?

## Let C = (-1, 3) be the point about which points A and B (and Daffy Duck) are rotated. Place point A at (1, 4) and B at (6, 2).

On Graph Paper, Rotate point A and point B 90 degrees counter-clockwise. What are the coordinates (x, y) of the image of A? What are the coordinates (x, y) of the image of B?