# 116 Chapter 6 Transformations and the Coordinate Plane

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3 118 Chapter 6 Transformations and the Coordinate Plane Chapter 6-2 Line Reflections Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [12] 1. If ABC has line smmetr onl when the median is drawn from verte B, what kind of triangle is ABC? (1) right (3) isosceles (2) scalene (4) equilateral 2. A line reflection preserves (1) distance and orientation. (2) angle measure and orientation. (3) distance but not angle measure. (4) distance and angle measure. 3. What kind of smmetr does the name TT have? (1) vertical line smmetr onl (2) horizontal line smmetr onl (3) both vertical and horizontal line smmetr (4) neither horizontal nor vertical line smmetr 4. Which letter has both vertical and horizontal line smmetr? (1) A (3) T (2) M (4) X 5. If ABC has line smmetr when an altitude is drawn from verte A or B, what kind of triangle is ABC? (1) right (2) isosceles (3) equilateral (4) scalene 6. In the given figure, m and k are smmetr lines for the regular pentagon ABCDE. A E B k Find E, the image of E under r m followed b r k. (1) A (3) C (2) B (4) D D C m

5 120 Chapter 6 Transformations and the Coordinate Plane Chapter 6-3 Line Reflections in the Coordinate Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [12] 1. What are the coordinates of B, the image of B(2, 1) after a reflection in the line? (1) ( 2, 1) (2) ( 1, 2) (3) (1, 2) (4) (2, 1) 2. What is the image of ( 4, 3) when reflected in the -ais? (1) ( 4, 3) (2) ( 3, 4) (3) (3, 4) (4) (4, 3) 3. The coordinates of P, the reflection of P(2, 6) in the line, are (1) ( 6, 2) (2) ( 6, 2) (3) (2, 6) (4) (6, 2) 4. When the points A( 5, 0), B(0, 5), C(5, 0), and D(0, 5) are joined, square ABCD is formed. Which of the following is not a line of smmetr? (1) 0 (2) 5 (3) (4) 5. If P, the image of point P under a reflection in the -ais, is in the second quadrant, in what quadrant is P, the image of P under a reflection in the line? (1) I (2) II (3) III (4) IV 6. If point A has coordinates (4, 5), what are the coordinates of A, the image of A when reflected first across 6 and then reflected across 2? (1) ( 4, 5) (2) (5, 3) (3) (5, 13) (4) (12, 5)

6 Chapter 6 Transformations and the Coordinate Plane 121 PART II Answer all questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar steps, answer with no work shown will receive onl 1 credit. [8] 7. The coordinates of the vertices of a rectangle are (1, 3), (7, 3), (7, 1), and (1, 1). a. Write the equation of the vertical line of smmetr of the rectangle. Answer: 4 b. Write the equation of the horizontal line of smmetr of the rectangle. Answer: 1 c. Find the area of the rectangle. Answer: 24 square units 8. Triangle PQR has coordinates P( 1, 3), Q(3, 7), and R(0, 6). a. State the coordinates of P Q R, the image of PQR under a reflection in the line. Answer: P (3, 1), Q (7, 3), R (6, 0) b. State the coordinates of P Q R, the image of P Q R under a reflection in the -ais. Answer: P ( 3, 1), Q ( 7, 3), R ( 6, 0)

7 122 Chapter 6 Transformations and the Coordinate Plane Chapter 6-4 Point Reflections in the Coordinate Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [12] 1. If the point ( 3, 2) is reflected in the origin, the coordinates of its image are (1) ( 3, 2) (3) (2, 3) (2) ( 2, 3) (4) (3, 2) 2. Which of the following graphs has point smmetr? (1) (2) 3. Point A (3, 5) is the reflection of point A( 1, 3). Which of the following is the point of reflection? (1) (2, 4) (2) (1, 4) (3) (1, 2) (4) (0, 0) 4. Which figure has no point smmetr? (1) square (2) rhombus (3) equilateral triangle (4) isosceles triangle 5. Which capital letter does not have point smmetr? (3) (1) S (3) C (2) N (4) H 6. Under a reflection in the origin, the image of (, ) is (4) (1) (, ) (2) (, ) (3) (, ) (4) (, )

8 Chapter 6 Transformations and the Coordinate Plane 123 PART II Answer all questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar steps, answer with no work shown will receive onl 1 credit. [8] 7. a. What is the image of P(3, 5) under a reflection in the origin? Answer: ( 3, 5) b. What is the image of Q(4, 0) under a reflection in the origin? Answer: ( 4, 0) c. Is the reflection of PQ in the -ais the same as the reflection of PQ in the origin? Justif our answer. Answer: No Eplanation: Under a reflection in the -ais, the image of P is ( 3, 5). 8. BAG with coordinates B(2, 1), A( 2, 3), and G(3, 5) is reflected through the origin. a. What are the coordinates of B A G, the image of BAG? Answer: B ( 2, 1), A (2, 3), G ( 3, 5) b. Graph both BAG and B A G. A B G G B A

10 Chapter 6 Transformations and the Coordinate Plane 125 Chapter 6-6 Rotations in the Coordinate Plane Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [12] 1. Which letter has rotational smmetr? (1) E (3) K (2) T (4) H 4. In the figure given, square ABCD is inscribed in circle. B A D C In the given figure, each polgon is the image of the other under a rotation about a fied point. Which is most likel the coordinates of the center of rotation? (1) (0, 0) (2) ( 3, 1) (3) ( 4, 2) (4) ( 5, 1) 3. What is the image of A(2, 5) under R 90? (1) ( 5, 2) (2) ( 2, 5) (3) (2, 5) (4) (5, 2) What is R 90 (A)? (1) A (3) C (2) B (4) D 5. Which figure has 120 rotational smmetr? (1) square (2) rhombus (3) parallelogram (4) equilateral triangle 6. If B is the image of A(2, 3) after a 90 rotation clockwise about the origin, the coordinates of B are (1) (3, 2) (3) ( 2, 3) (2) ( 2, 3) (4) ( 3, 2)

12 Chapter 6 Transformations and the Coordinate Plane 127 Chapter 6-7 Glide Reflections Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [12] 1. Which propert is not preserved b a glide reflection? (1) betweenness (2) angle measure (3) orientation (4) collinearit 2. Find the image of point P(5, 4) under the glide reflection T 23,23 followed b r =. (1) (2, 1) (2) (1, 2) (3) ( 1, 2) (4) ( 12, 15) 3. A glide reflection is defined b r 521 followed b T a,b. If the image of P( 5, 2) is P (3, 8) under this transformation, what are the values of a and b? (1) a 10, b 0 (2) a 10, b 8 (3) a 0, b 10 (4) a 8, b Under a glide reflection, r =1 is followed b T a,b.if A(6, 4) A ( 7, 2) under this transformation, what are the values of a and b? (1) a 0, b 13 (2) a 6, b 13 (3) a 13, b 0 (4) a 13, b 6 5. Under a glide reflection, the image of A(4, 3) is A ( 4, 3) and the image of B( 7, 8) is B (7, 2). If the line of reflection is vertical, which of the following is the line of reflection? (1) 1 (2) 0 (3) 1 (4) 0 6. Under a glide reflection, the image of Q(0, 2) is Q (4, 2). If the translation is T 2,2, which of the following is the line of reflection? (1) 2 (2) 2 (3) (4)

13 128 Chapter 6 Transformations and the Coordinate Plane PART II Answer all questions in this part. Each correct answer will receive 4 credits. Clearl indicate the necessar steps, answer with no work shown will receive onl 1 credit. [8] 7. Given: DE with D(2, 6) and E(5, 10) Graph and state the coordinates of the endpoints of: a. DrEr, the image of DE under the reflection r. Answer: D (6, 2), E (10, 5) b. DsEs, the image of DrEr after the translation T 3,3. Answer: D (9, 5), E (13, 8) D E E D Given: ABC with A( 6, 3), B( 1, 5), and C( 3, 8). Graph and state the coordinates of the vertices of: a. A B C, the image of ABC under the translation T 3,0. Answer: A ( 3, 3), B (2, 5), C (0, 8) b. A B C, the image of A B C under the reflection r =2. Answer: A ( 3, 1), B (2, 1), C (0, 4) C C A 3 2 A B B

15 130 Chapter 6 Transformations and the Coordinate Plane Chapter 6-9 Transformations as Functions Section Quiz [20 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [20] 1. Which transformation is a direct isometr? 6. (1) D 3 (3) D 22 (2) r -ais (4) T 2,3 2. The graph of g() is shown. g() Which of the following graphs represents the image of the given triangle under the composition r 5 + R 908? (1) Which of the following graphs represents r -ais + r -ais (g())? (1) (3) (2) (2) (4) 3. What is the image of point (2, 2) under the composition r -ais + R 908? (1) (2, 2) (3) ( 2, 2) (2) (2, 2) (4) ( 2, 2) (3) 4. If the coordinates of P are ( 3, 7), what are the coordinates of D 2 + r 5 (P)? (1) ( 14, 6) (3) (6, 14) (2) ( 6, 14) (4) (14, 6) 5. Which transformation is an opposite isometr? (1) dilation (3) rotation of 90 (2) line reflection (4) translation (4)

20 Chapter 6 Transformations and the Coordinate Plane 135 Chapter 6 Transformations and the Coordinate Plane Cumulative Review [40 points] PART I Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. [16] 1. If B is the midpoint of line segment AC and D is the midpoint of line segment AB, which statement is true? (1) AB CB (3) AC AB (2) AD BD (4) DC 3BD 2. In the given figure, l, m, and n are lines with l m. l n m 5. The triangle with vertices at (0, 0), (6, 0), and ( 2, 2) is (1) right (3) scalene (2) isosceles (4) equilateral 6. Which of the following is a direct isometr? (1) D 2 (3) r -ais (2) r (4) R In the given figure, BED, CEA, B D, and E is the midpoint of BD. B C Which angles are complementar? E (1) 1 and 3 (3) 2 and 3 (2) 1 and 2 (4) 3 and 5 A D 3. AB h and AC h are opposite ras if and onl if (1) B and C are on the same side of A. (2) B is between A and C. (3) A is between B and C. (4) A, B, and C are collinear. 4. Which statement is the converse of If two sides of a triangle are congruent, then the triangle is isosceles? (1) If a triangle is not isosceles, then two sides of the triangle are not congruent. (2) If two sides of a triangle are not congruent, then the triangle is not isosceles. (3) If a triangle is isosceles, then two sides of the triangle are congruent. (4) If two sides of a triangle are congruent, then the triangle is not isosceles. Which postulate justifies BEC DEA? (1) SSS (3) SSA (2) ASA (4) SAS 8. If the point (6, 0) is mapped onto point (6, 3) b some line reflection, we could describe the line of reflection as (1) the -ais. (2) parallel to the -ais. (3) parallel to the -ais. (4) the line.

22 Chapter 6 Transformations and the Coordinate Plane Given: PQ > QR and PT > RT Q Prove: QT bisects PQR. T Proof: Statements P Reasons R 1. PQ > QR and PT > RT 1. Given. 2. QT > QT 2. Refleive propert of congruence. 3. PQT RQT 3. SSS. 4. PQT RQT 4. Corresponding parts of congruent triangles are congruent. 5. QT bisects PQR. 5. Definition of angle bisector. PART IV Answer all questions in this part. Each correct answer will receive 6 credits. Clearl indicate the necessar steps, answer with no work shown will receive onl 1 credit. [12] 13. a. The measures of the acute angles of a right triangle are in the ratio 1 : 4. What is the number of degrees in the measure of each of the acute angles? Answer: 18 and 72 Solution: b. In isosceles triangle PQR, QP > QR,m Q 5 13, and m P 2 7. Find the measure of each angle in PQR. Answer: m Q 98, m P m R 41 Solution: (17) , (17)

23 138 Chapter 6 Transformations and the Coordinate Plane 14. Given: AE h and GF h, HC > GD, 1 2, and AB > CD. Prove: H G H G A B 1 C 3 D 2 E Proof: F Statements Reasons 1. HC > GD, 1 2, and AB > CD 1. Given Vertical angles are congruent Transitive propert of congruence. 4. AC 5 AB 1 BC, BD 5 BC 1 CD 4. Partition postulate. 5. AB 1 BC > BC 1 CD 5. Addition postulate. 6. AC > BD 6. Substitution postulate. 7. AHC BGD 7. SAS. 8. H G 8. Corresponding parts of congruent triangles are congruent.

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