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Geometry Transformations ~1~ NJCTL.org

Transformations

Transformations: CLASSWORK Tell whether the transformation appears to be a rigid motion. Explain. 1. 2. Preimage Image Preimage Image 3. Identify the type of transformation. What is the image of segment FG?

4. Identify the type of transformation. What is the image of angle J?

Geometry Transformations ~2~ NJCTL.org

Transformations: HOMEWORK Tell whether the transformation appears to be a rigid motion. Explain. 1. 2. Preimage Image Preimage Image 3. Identify the type of transformation. What is the image of segment QR?

4. Identify the type of transformation. What is the image of angle T?

Geometry Transformations ~3~ NJCTL.org

Translations: CLASSWORK

Graph the image of each figure under the given translation.

1. T (ABC) 2. T (JKLM)

3. Write a rule to describe the translation.

4. If T (QRST) = QRST, what translation maps QRST onto QRST?

Geometry Transformations ~4~ NJCTL.org

5. XYZ has coordinates X(2, 3), Y(1, 4), and Z(8, 9). A translation maps X to X(4, 8). What are the coordinates for Y and Z for this translation?

6. Write three different translation rules for which the image of ABC has a vertex at the origin.

Translations: Homework

Graph the image of each figure under the given translation. 1. T (DEF) 2. T (WXYZ)

Geometry Transformations ~5~ NJCTL.org

3. Write a rule to describe the translation.

4. If T (LMN) = LMN, what translation maps LMN onto LMN?

5. ABC has coordinates A(2, 3), B(4, 2), and C(3, 0). After a translation the coordinates of A are (6, 2). What are the coordinates of B and C?

6. Write three different translation rules for which the image of BCD has a vertex at the origin.

Geometry Transformations ~6~ NJCTL.org

Reflections: CLASSWORK For numbers 1-6 find the coordinates of each image. 1. Rx-axis (A) 2. Ry-axis (B) 3. Ry = x (C) 4. Rx = 2 (D) 5. Ry= -1 (E) 6. Rx = -3 (F)

7. Given points A(3, 3), B(5, -2), and C(4, 4), graph ABC and its reflection image as indicated. a. Ry-axis (ABC) b. Rx-axis (ABC)

Geometry Transformations ~7~ NJCTL.org

c. Rx = 1(ABC) d. Ry = 2(ABC)

Draw the line of reflection you can use to map one figure onto the other.

8. 9.

10. Find the image of J(-2, 1) after two reflections, first across line 1, and then across line 2.

a. 1 : x = 2, 2 : y-axis

b. 1 : y = 1, 2 : y-axis

c. 1 : y = 2, 2 : x-axis

d. 1 : x = 1, 2 : y = 3

11. Give an example of a place you may see a geometric reflection in everyday life. Explain.

Geometry Transformations ~8~ NJCTL.org

Identify all of the lines of symmetry for the given shape. 12. 13. 14. 15. 16. 17.

Reflections: HOMEWORK

For numbers 1-6 find the coordinates of each image. 1. Rx-axis (A) 2. Ry-axis (B) 3. Ry = x (C) 4. Rx = 3 (D) 5. Ry= 2 (E) 6. Rx = -1 (F)

Geometry Transformations ~9~ NJCTL.org

7. Given points D(-2, 1), E(1, 3), and F(2, -2), graph DEF and its reflection image as indicated. a. Ry-axis (DEF) b. Rx-axis (DEF)

c. Rx = 2(DEF) d. Ry = 1(DEF)

Geometry Transformations ~10~ NJCTL.org

Draw the line of reflection you can use to map one figure onto the other.

8. 9.

10. Find the image of K(4, -3) after two reflections, first across line 1, and then across line 2.

a. 1 : x = 2, 2 : y-axis

b. 1 : y = 1, 2 : y-axis

c. 1 : y = 2, 2 : x-axis

d. 1 : x = 1, 2 : y = 3

11. Give an example of a place you may see a geometric reflection in everyday life (Different than your classwork answer). Explain Identify all of the lines of symmetry for the given shape. 12. 13. 14. 15. 16. 17.

Geometry Transformations ~11~ NJCTL.org

Rotations: CLASSWORK Draw the image of each figure for the given rotation about P. Use prime notation to label the vertices of the image.

1. r(-60, P)(ABC)

2. r(85, P)(ABC)

3. Point O is the center of regular pentagon JKLMN. Find the image of the given point or segment for the given rotation. (counterclockwise)

a. r(144, O)(K)

b. r(72, O)(N)

c. r(216, O)(ML)

d. r(360, O)(JN)

e. r(288, O)(JO)

Geometry Transformations ~12~ NJCTL.org

4. ABC has vertices A(2, 2), B(3, 2), and C(1, 3). a. Graph r(270, O)(ABC). b. Graph r(180, O)(ABC).

c. Graph r(90, O)(ABC).

5. The vertices of ABCD have coordinates A(2, 6), B(-3, 4), C(-3, -5), and

D(4, -2). What are the coordinates of the vertices of r (180, O)(ABCD)?

Geometry Transformations ~13~ NJCTL.org

6. The vertices of r(270, O) (DEFG) have coordinates D(4, 5), E(4, -3), F(-2, -3), and G(-2, 5). What are the coordinates of the vertices of DEFG?

7. ABCD has vertices A(4, 2), B(2, 2), C(4, 2), and D(2, 2). Which of the following quadrilaterals is r(180, O)(ABCD)?

a. ABCD b. BCDA c. CDAB d. DABC

8. FGH has vertices F(1, 2), G(0, 0), and H(3, 1). What are the coordinates of the vertices of r(270, G)(FGH)? Do the following figures have rotational symmetry? If yes, what is the degree of rotation? 9. 10. 11. Rotations: HOMEWORK Draw the image of each figure for the given rotation about P. Use prime notation to label the vertices of the image. 1. r(-90, P)(ABC)

Geometry Transformations ~14~ NJCTL.org

2. r(110, P)(ABC)

3. Point O is the center of regular hexagon ABCDEF. Find the image of the given point or segment for the given rotation. (counterclockwise)

a. r(120, O)(F)

b. r(180, O)(B)

c. r(300, O)(BC)

d. r(360, O)(FE)

e. r(60, O)(E)

f. r(240, O)(AB) 4. Quadrilateral DEFG has vertices D(2, 3), E(4, -2), F(7, -2), and G(5, 2). a. Graph r(270, O)(DEFG). b. Graph r(180, O)(DEFG).

Geometry Transformations ~15~ NJCTL.org

c. Graph r(90, O)(DEFG).

5. The vertices of PQRS have coordinates P(1, 5), Q(3, 4), R(2, 4), and S(3, 2). What are the

coordinates of the vertices of r (90, O)(PQRS)?

6. The vertices of r(270, O) (KLMN) have coordinates K(3, 2), L(2, 3), M(4, 2), and N(2, 4). What are the coordinates of the vertices of KLMN?

7. The vertices of quadrilateral ABCD have coordinates A(4, 3), B(3, 4), C(4, 3), and D(3, 4). Explain how the transformation r(90, O)(ABCD) = BCDA can be used to show that the quadrilateral is square.

Geometry Transformations ~16~ NJCTL.org

8. RST has vertices at R(0, 3), S(4, 0), and T(0, 0). What are the coordinates of the vertices of r(-270,T)(RST)?

Do the following figures have rotational symmetry? If yes, what is the degree of rotation?

9. 10. 11.

Geometry Transformations ~17~ NJCTL.org

Compositions of Transformations: CLASSWORK

Find the image of each letter after the transformation Rm R. Is the resulting transformation a translation or a rotation? For a translation, describe the distance and direction. For a rotation, tell the center of rotation and the angle of rotation.

1. l 2.

K m

For numbers 3 6 Graph ABC and its glide reflection image. A(-3, 3), B(0, 1) and C(-1,-4)

3. (Ry-axis T)(ABC) 4.(Ry=1 T)(ABC)

J

l 60 m P

Geometry Transformations ~18~ NJCTL.org

5. (Rx=2 T)(ABC) 6. (Ry=x T)(ABC)

7. Lines and m intersect at point P and are perpendicular. If a point Q is reflected across and then across m, what transformation rule describes this composition? 8. Graph AB and its image AB after a reflection first across 1 and then across 2. Is the resulting transformation a translation or a rotation? For a translation, describe the direction and distance. For a rotation, tell the center of rotation and the angle of rotation.

A(3, 4), B(1, 0); 1 : x = 1; 2 : y = 1

Geometry Transformations ~19~ NJCTL.org

9. P maps to P(2, 3) by the given glide reflection. What are the coordinates of P? (Rx-axis T )(P) Compositions of Transformations: HOMEWORK

Find the image of each letter after the transformation Rm R. Is the resulting transformation a translation or a rotation? For a translation, describe the distance and direction. For a rotation, tell the center of rotation and the angle of rotation.

1. 2.

For numbers 3 6 Graph DEF and its glide reflection image. D(0, 2), E(2, 4) and F(4,0)

3. (Rx-axis T)(DEF) 4. (Ry=2 T)(DEF)

m

A l K

N l

m

Geometry Transformations ~20~ NJCTL.org

5. (Rx=1 T)(DEF) 6.. (Ry=x T)(DEF)

7. A triangle is reflected across line and then across line m. If this composition of reflections is a translation, what is true about m and ?

8. Graph AB and

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