<p>Transformations – Unit Review 1. For each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box.</p><p>The image and The image and Lengths of Measures of preimage are preimage are segments are angles are similar but not congruent preserved preserved congruent Translation</p><p>Reflection</p><p>Rotation Glide Reflection Dilation</p><p>2. Identify the rigid motion that maps the figure on the right onto the figure on the left. a. b. </p><p>3. ∆R’S’T’ is a translation image of ∆RST. What is a rule for the translation?</p><p>4. Find the coordinates of the vertices of each image.</p><p> a. Rx-axis(ABCD) b. Ry-axis(ABCD)</p><p> c. Ry=x(ABCD) d. Ry=2 (ABCD)</p><p>Geometry – Transformations ~1~ NJCTL.org e. Rx=-1(ABCD) f. r(270°, O)(ABCD)</p><p> g. r(180°, O)(ABCD) h. r(90°, O)(ABCD)</p><p> i. D5(ABCD) j. T<2, -5> (ABCD)</p><p> k. (Ry = -2 ○ T<-4, 0>)(ABCD)</p><p>5. Draw the line of reflection you can use to map one figure onto the other.</p><p>6. Find the image of M(-1, 4) after two reflections, first across line ℓ1, and then across line ℓ2.</p><p> a. ℓ1 : x = 2, ℓ2 : y-axis b. ℓ1 : y = –2, ℓ2 : x-axis</p><p>7. The letter H is reflected across the line x = -2 and then line x = 4. Describe the resulting transformation. </p><p>8. The letter J is reflected across line m and then line n. Describe the resulting transformation. </p><p>Geometry – Transformations ~2~ NJCTL.org 9. Point K is the center of regular quadrilateral ABCD. Find the image of the given point or segment for the given rotation. (counterclockwise) a. r(90°, K)(K)</p><p> b. r(270°, K)(N)</p><p> c. r(180°, K)(ML)</p><p> d. r(360°, K)(JN)</p><p> e. r(90°, K)(JO)</p><p>10. Graph ∆ABC and its glide reflection image. A(-5, 3), B(1, 2) and C(-2,-4)</p><p> a. (RX-axis ○ T<2, 1>)(∆ABC) 4.(Ry=2 ○ T<–1, 0>)(∆ABC)</p><p>Geometry – Transformations ~3~ NJCTL.org 11. Write a congruence statement for the two figures in the coordinate grid. Then write a congruence transformation that maps one figure to the other.</p><p>12. Write a similarity statement for the two figures in the coordinate grid. Then write a similarity transformation that maps one figure to the other.</p><p>13. The solid-line figure is a dilation of the dashed-line figure with center of dilation P. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?</p><p>14. A dilation has center (0, 0). Find the image of each point for the given scale factor.</p><p>Geometry – Transformations ~4~ NJCTL.org a. P(-2, 4); D4(P) b. A(10, 4); D1/4(A) c. K(3, -6); D0.5(K)</p><p>15. Does the figure have reflectional symmetry? If so draw the line(s) of symmetry. Does the figure have rotational symmetry? If so state the degree of rotation. </p><p>16. Draw the image of the figure for the given rotation about P. Use prime notation to label the vertices of the image.</p><p> r(100°, P)(∆ABC)</p><p>Geometry – Transformations ~5~ NJCTL.org ANSWER KEY Transformations – Unit Review 1. For each transformation in the table below, indicate which properties are true by placing a check mark in every appropriate box.</p><p>The image and The image and Lengths of Measures of preimage are preimage are segments are angles are similar but not congruent preserved preserved congruent Translation X X X</p><p>Reflection X X X</p><p>Rotation X X X Glide X X X Reflection Dilation X X</p><p>2. Identify the rigid motion that maps the figure on the right onto the figure on the left. a. b. </p><p>Rotation Reflection</p><p>3. ∆R’S’T’ is a translation image of ∆RST. What is a rule for the translation?</p><p>T<-7, 3>(∆RST) = ∆R’S’T’ </p><p>4. Find the coordinates of the vertices of each image.</p><p> a. Rx-axis(ABCD) b. Ry-axis(ABCD)</p><p>A(-4, -3), B(1, -6), C(4, -5), D(0, -2) A(4, 3), B(-1, 6), C(-4, 5), D(0, 2)</p><p> c. Ry=x(ABCD) d. Ry=2 (ABCD)</p><p>A(3, -4), B(6,1), C(5, 4), D(2, 0) A(-4, 1), B(1, -2), C(4, -1), D(0, 2)</p><p> e. Rx=-1(ABCD) f. r(270°, O)(ABCD)</p><p>Geometry – Transformations ~6~ NJCTL.org A(2, 3), B(-3, 6), C(-6, 5), D(1, 2) A(-3, -4), B(-6, 1), C(-5, 4), D(-2, 0)</p><p> g. r(180°, O)(ABCD) h. r(90°, O)(ABCD)</p><p>A(4, -3), B(-1, -6), C(-4, -5), D(0, -2) A(3, 4), B(6, -1), C(5, -4), D(2, 0)</p><p> i. D5(ABCD) j. T<2, -5> (ABCD)</p><p>A(-20, 15), B(5, 30), C(20, 25), D(0, 10 A(-2, -2), B(2, 1), C(6, 0), D(2, -3)</p><p> k. (Ry = -2 ○ T<-4, 0>)(ABCD)</p><p>A(-8, -7), B(-3, -10), C(0, -9), D(-4, -6)</p><p>5. Draw the line of reflection you can use to map one figure onto the other.</p><p>6. Find the image of M(-1, 4) after two reflections, first across line ℓ1, and then across line ℓ2.</p><p> a. ℓ1 : x = 2, ℓ2 : y-axis b. ℓ1 : y = –2, ℓ2 : x-axis</p><p>(-5, 4) (-1, 8)</p><p>7. The letter H is reflected across the line x = -2 and then line x = 4. Describe the resulting transformation. A translation 12 units to the right. </p><p>8. The letter J is reflected across line m and then line n. Describe the resulting transformation. 150 degree rotation clockwise</p><p>Geometry – Transformations ~7~ NJCTL.org 9. Point K is the center of regular quadrilateral ABCD. Find the image of the given point or segment for the given rotation. (counterclockwise) a. r(90°, K)(A) D</p><p> b. r(270°, K)(D) A</p><p> c. r(180°, K)(DC) AB</p><p> d. r(360°, K)(KB) KB</p><p> e. r(90°, K)(BC) AB</p><p>10. Graph ∆ABC and its glide reflection image. A(-5, 3), B(1, 2) and C(-2,-4)</p><p> a. (RX-axis ○ T<2, 1>)(∆ABC) 4.(Ry=2 ○ T<–1, 0>)(∆ABC)</p><p>11. Write a congruence statement for the two figures in the coordinate grid. Then write a congruence transformation that maps one figure to the other.</p><p>∆ABC ≅ ∆FGH;</p><p>Sample: Rx-axis○ T<3, -1>(∆ABC) = ∆FGH</p><p>Geometry – Transformations ~8~ NJCTL.org 12. Write a similarity statement for the two figures in the coordinate grid. Then write a similarity transformation that maps one figure to the other.</p><p>∆TUV ~ ∆XYZ; Sample: T<-4, -3> ○D2(∆TUV) = ∆XYZ</p><p>13. The solid-line figure is a dilation of the dashed-line figure with center of dilation P. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation?</p><p> enlargement; 7/4</p><p>14. A dilation has center (0, 0). Find the image of each point for the given scale factor.</p><p> a. P(-2, 4); D4(P) b. A(10, 4); D1/4(A) c. K(3, -6); D0.5(K)</p><p>(-8, 16) (5/2, 1) (1.5, -3)</p><p>15. Does the figure have reflectional symmetry? If so draw the line(s) of symmetry. Does the figure have rotational symmetry? If so state the degree of rotation. </p><p>180 degree rotational symmetry </p><p>16. Draw the image of the figure for the given rotation about P. Use prime notation to label the vertices of the image.</p><p> r(100°, P)(∆ABC) </p><p>Geometry – Transformations ~9~ NJCTL.org</p>