# Lesson 1 Centered! Develop Understanding

Find the area and circumference of each circle. Leave

### 1.

Area:

Circumference:

### 2.

Area:

Circumference:

### 3.

Complete the chart by filling in the area and circumference for each circle. Leave

Radius | |||||
---|---|---|---|---|---|

Area | |||||

Circumference |

### 4.

What patterns do you notice in the table?

In each figure, locate and mark at least four possible centers of rotation that would work for rotating the image point to the pre-image point.

### 5.

### 6.

### 7.

### 8.

Complete the sentence:

The center of rotation will always be located on the of the segment that connects two corresponding points.

Find the center of rotation for each set of rotated figures. Identify the approximate center of rotation as a point.

### 9.

Center of rotation:

### 10.

Center of rotation:

### 11.

Center of rotation:

### 12.

Find the center of rotation of the rotated figures by connecting corresponding points and constructing the perpendicular bisectors. Identify the approximate center of rotation as a point.

Label the center of rotation as point

. Use a compass to draw a circle with center at point and with radius . Are , , , and also radii of circle ? If you were precise in your construction of the center of rotation all of the aforementioned segments will be the same distance from the center and are, therefore, radii of the circle. Also, and will be chords of the same circle.

Center of rotation:

### 13.

You can use the information from problem 12 to find the center of a circle. Label the center as point

Each problem shows two similar figures. For each pre-image and image indicate whether the scale factor (

### 14.

Is

Why?

Scale factor:

### 15.

Is

Why?

Scale factor:

### 16.

Is

Why?

Scale factor:

### 17.

Is

Why?

Scale factor:

Each pair of images is the result of a dilation. For each pair of figures given, determine the coordinates for the center of dilation.

### 18.

Center of dilation:

### 19.

Center of dilation:

### 20.

Center of dilation: