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Lesson 1 Centered! Develop Understanding

Ready

Find the area and circumference of each circle. Leave in your answers.

1.

Circle with radius 5 cm

Area:

Circumference:

2.

Circle with radius 8 in

Area:

Circumference:

3.

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

five circles with radius 1m, 2m, 3m,4m,5m

Radius

Area

Circumference

4.

What patterns do you notice in the table?

Set

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.

Point A(7,2) Point A'(11,2)x555101010y555

6.

Point A (7,2) Point A' (3,6)x555y555000

7.

Point P (-6,3) Point P'(-2,5)x–5–5–5y555000

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:

Trapezoid WXYZ W(2.4, 1), X(.4,1), Y(1,2), Z(.8,2) Trapezoid W'X'Y'Z' W'(2.2,2.4) X'(2.2,4.2) Y'(3.2,3.8) Z'(3.2,3)x111222333444y111222333444555000

10.

Center of rotation:

Rectangle WXYZ and Rectangle W'X'Z'Y'x111222333444555y111222333444555000

11.

Center of rotation:

Triangle ABC and Triangle A'B'C'x–5–5–5555y–5–5–5555000

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:

Line Segment GH and G'H'x–3–3–3–2–2–2–1–1–1111222333y–4–4–4–3–3–3–2–2–2–1–1–1111222333000

13.

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

Circle with Chord GH and Chord JK

Go

Each problem shows two similar figures. For each pre-image and image indicate whether the scale factor () should be greater than or less than . Justify your answer. Then determine the scale factor between the two figures.

14.

Triangle PQR and Triangle P'Q'R'x111222333444555y111222000

Is or ?

Why?

Scale factor:

15.

Triangle XYZ X(2,3) Y(4,3) and Z (3,1). Triangle X'Y'Z' X'(-4,3) Y'(-1,3) and Z'(-2.5,0)x–5–5–5555y555000

Is or ?

Why?

Scale factor:

16.

Circle C with radius CN and Circle C' with radius C'N'x555y555000

Is or ?

Why?

Scale factor:

17.

Larger Circle with diameter A'B' over rectangle and smaller circle with diameter AB over rectangle.

Is or ?

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.

Quadrilateral ABCD B(5,2) C(6,3) A(4,3) and D(5,4) Quadrilateral A'B'C'D' A'(2,9) B'(5,6) C'(8,9) D'(5,12)x555101010y555101010000

Center of dilation:

19.

Pentagon ABCDE inscribed in Pentagon A'B'C'D'E'x–10–10–10–5–5–5y–10–10–10–5–5–5000

Center of dilation:

20.

Triangle ABC with interior line segment A'B' parallel to AB. x555y555000

Center of dilation: