2D Geometry Questions and Answers

3 rotation 90 clockwise about the origin A B X

ane Translate a units to the right Translate a units to the left Translate b units up Translate b units down Rules for Reflection on a Coordinate Plane Reflection across the x axis Reflection across the y axis Reflection across line y x Reflection across line y x Rules for Rotation on a Coordinate Plane 90 rotation counterclockwise 180 rotation 270 rotation counterclockwise 360 rotation Transformation Rule x y Figure 1 x y x a y x y x a y x y x y b x y x y b Coordinate Notation 1st Transformation x y x y x y x y x y y x x y y x Coordinate Notation x y y x x y x y x y y x x y x y 2nd Transformation 2 Figure 2 P 11 2 B 0 2 2 8 NYN 2 0 2 0 2 41YB N 4 4 M O 2 AD 2 P 4 X X 4

3 AABC and AA B C are shown on the coordinate plane Devon claims that a sequence of rigid motions carries AABC onto AA B C Which actions could he take to prove his claim 8 6 4 B B Sot C 6 4 N 0 A 2

1 ADEF AWVU D W 3 Which of the following is NOT true about congruent triangles AABC and ADEF A AB DE B BC FD C ZABC ZDEF D ZCAB LFDE Given the information above the following sides are are equal equal DE 5 Which of the following is NOT true about congruent quadrilaterals QRST and WXYZ A RS XY B ZSTQZYZW C ZRQTZXWZ D ST XW 2 LABC LLMN Cou M Given the information above the following angles LACB L 4 Which of the following is NOT true about congruent triangles AAGK and AQVZ A ZKGA LZVQ B KG ZV C AG VZ D ZGKA ZVZQ 6 Which of the following is NOT true about congruent polygons JKLMN and TUVWX A LMN LUVW B MN WX C LK VU D ZMNJ WXT Optional Complete problems 1 5 8 13 17 18 from your textbook on separate lined paper When you are finished check the odd problems for solutions at the back of the textbook

Your Turn 1 AABC DEF Find the length of CA DE EF Find the angle measure of 2A 2B 2C re 2 6 cm B 3 7 cm 3 5 cm 42 The side lengths are follows CA 3 5 cm DE 2 6 cm EF 3 7 cm a LV b OP C ST D 73 Since AABC ADEF these six facts are always true Corresponding sides are congruent 65 Corresponding angles are congruent The angle measures are as follows mLA 73 m2B 65 m2C 42 2 The following figures are congruent Find the measure of the following 0 112 43 51 km 69 N 21 km M bigmund V 39 km 16 km 43 MATRASONE S ilmoge 136 D ogla 69 hogestio Need help Visit the L4L Math Resources Website http Bit ly L4Lmath to find videos and other resources for this lesson

Your Turn Quadrilateral GHJK quadrilateral LMNP Find the given side length or angle measure 18 cm 10y 1 Find LM 4x 3 cm 9y 17 Your friend s work H m2H mzL 9y 17 10y 6x13 cm 3 Your friend tries to solve mZH Your friend did not set up to solve for mzH correctly Explain to your friend their misunderstanding and how to set it up correctly Explain to your friend their misunderstanding and how to set it up correctly 11y 1 M 2 Find m2H

Por 1 2 draw the image after the given transformations You can create a table to organize your work Don t forget to label the points for the first and second image 10 1 Reflect Rectangle ABCD across the y axis then translate it using the following rule x y x 4 y 3 B D C N 0 A B 10 C D 3 x y x 2 y x y A B C D Describe the type of transformations of 2 Rotate Rectangle ABCD 90 counterclockwise Then translate it along the vector 3 4 B D C 2nd 2 O 2 2 A N B C D A B C D 4 x y x y 8 x y Describe the type of transformations 1st J

Read Explore and complete the following adapted from Lesson 3 3 Show all your work AABC and ADEF are congruent meaning AABC can be mapped onto ADEF by a sequence of rigid motions F C DE Rigid motions preserve the measure of the sides and the measure of the angles Determine which sides and angles from ADEF match up with AABC by completing the following AB BC LA 211 B 211 LB If you know that AABC ADEF what six congruence statements about segments and angles can you write 211 AC 211 LC 211 211 Examples of congruence statements FH HJ LF 4

1 Complete the following to co O Yes O No AQRS is the image of ALMN under a sequence of transformations Can each of the following sequences be used to create the image AQRS from the preimage ALMN Select yes or no a Reflect across the y axis and then translate along the vector 0 4 b Translate along the vector 0 4 and then reflect across the y axis c Rotate 90 clockwise about the origin reflect across the x axis and then rotate 90 counterclockwise about the origin O No Yes O No d Rotate 180 about the origin reflect across the x axis and then translate along the vector 0 4 Yes Yes O No S 7 M 4 2 0 2 4 4 R 2 Q HOS 4 84 N X

1 Reflect AABC over the x axis and rotate 180 degrees around the origin ty 8 6 4 2 Transformation rule Preimage ABC A 1 2 B B 3 4 C 2 5 N 4 6 6 4 2 0 O VAL 2 4 Image A B C 6 8 x1 X Image A B C

Lesson 3 2 Homework HW Complete problems 1 6 for independent practice When you are finished check the solutions with your teacher 3 Choose the two correct transformations for RSTU to R S T U A Rotation 180 clockwise OB Reflection across y x DC Reflection across y x OD Rotation 180 counterclockwise 5 Choose the two transformations for HIG to HT G A Rotation 90 clockwise OB Reflection across y x OC Reflection across y x OD Rotation 270 counterclockwise 4 Describe the transformation used for 47 a CDEF to C D E F A Reflection across the y axis B Reflection across y 1 C Reflection across x 1 OD Reflection across the x axis 6 Describe the transformation used for RST to R S T A Reflection across the x axis B Reflection across the y axis C Rotation 180 clockwise D Reflection across y x Optional Complete problems 1 3 5 7 18 from your textbook on separate lined paper

2 1 2 1 3 Bank You may use each statement once Hot Given ASVT ASWT Prove ST bisects ZVSW 2 1 ASVT ASWT Given Quadrilateral ABCD quadrilateral EFGH AD CD Prove AD GH Def of Angle Bisector AD CD LTSV LTSW Transitive Property of Congruence Statements 3 ST bisects VSW 4 AD GH Statements Statement Bank 3 Given Def of Segment Bisector CD GH Quadrilateral ABCD QuadrilateralEFGH 1 2 Corresponding parts of congruent figures are congruent 4 D Reasons BE H Reasons G 1 Given 2 Given 3 Corresponding parts of congruent figures are congruent

Your Turn Formos The figures shown are congruent Find a rigid motion that maps one figure to the other Give coordinate notation for the transformations you use 1 ABCD WXYZ Part 1 Figure ABCD can be mapped onto WXYZ by A Rotation B Reflection DC Translation OD The figures are not congruent Part 2 The coordinate notation is 2 ABCDE PQRST Part 1 ABCDE can be mapped onto PQRST by A Rotation B Reflection DC Translation D The figures are not congruent Part 2 The coordinate notation is 20 000 8 8 Y 4 X B 80 4 R ty A 0 Z4 4 A ty E 0 2N 4 D 8 W 8 S DX 4 8

7 8 Identify the surface whose equation is given p cos 1 Answer Horizontal plane ha

HW 0 Complete problems 1 6 for independent practice When you are finished check the solutions with your teacher Draw the image of the figure under the given rotation Create a table to find the coordinates of the image after performing the transformation 1 rotation 180 about the origin 3 rotation 90 clockwise about the origin 5 rotation 90 about the origin 2 rotation 180 about the origin 4 rotation 270 about the origin 6 rotation 180 about the origin G H Optional Complete problems 2 7 15 from your textbook on separate lined paper D When you are finished check the odd problems for solutions at the back of the textbook

1 Match the quote to the correct coordinate notation One is done for you A Rules for Rotation on a Coordinate Plane 90 rotation clockwise or 270 counterclockwise x y y x 90 rotation counterclockwise or 270 clockwise x y y x 180 rotation G 360 rotation x y x y For 2 3 draw the image of the figure under the given rotation 2 APQR 90 about the origin ty 4 D x y x y 4 2 4 2 E 2 Quadrilateral DEFG 180 about the origin 0 P 2 R Q X Quote A To rotate the figure all x values will be they values all y values will be the opposite sign the x values B To rotate the figure all x values will take the opposite sign all y values will take the opposite sign C To rotate the figure all x values will take the opposite sign of the y values all y values will take the x values D To rotate the figure all x values will remain the same all y values will remain the same When no direction is specified you can assume the rotation is counterclockwise Transformation Rule x y Preimage Coordinates x y Transformation Rule x y Preimage Coordinates x y Image Image

I can develop definitions of rel perpendicular lines parallel lines and line segments Lesson 2 2 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint below Complete the Lesson Reflection above by circling your current understanding of the Learning Goal 1 Draw the image of AABC after the reflection across line 1 Make sure to label appropriately A A OB C B 2 Using your answer above which of the following points does NOT move at all after the reflection 3 Are all reflections considered a rigid motion Explain why or why not by explaining its effects on a figure s angles and line segments

5 Reflect the shape below across the line x 2 Label the new coordinates M C N DA OB Oc 6 O 20 2 2 4 Transformation Rule x y 6 10 7 The following triangle is reflected across its own line BD Which of the following is NOT true B D 12 Image B and B are in the same spot C and C are in the same spot D and D are in the same spot 6 Reflect the shape below across the line y 3 Label the new coordinates Image 6 S G A OB c OD J 2 2 0 2 4 K 2 H 4 Transformation Rule x y 8 The following rectangle is reflected across its own line QR Which of the following is true Mark ALL that apply 6 T QR is in the same spot R and R are in the same spot ST is parallel to ST R is the midpoint of TT ptional Complete problems 1 2 4 6 9 10 12 from your textbook on separate lined paper When you are finished check the odd problems for solutions at the back of the textbook R

Lesson 2 2 Homework D 6 HW 1 Reflect the shape below across the x axis Label the new coordinates and write the transformation rule felona 6 4 G A B C y E D 46 20 4 2 20 2 4 Transformation Rule x y 6 2 2 3 Reflect the shape below across the x axis Label the new coordinates and write the transformation rule Complete problems 1 8 for independent practice When you are finished check the solutions with your teacher 2 H 2 A 4 6 ransformation Rule x y F Image 6 Image 2 Reflect the shape below across the y axis Label the new coordinates and write the transformation rule Image 6 4 2 you 8 6 6 4 6 4 2 0 W 4 14 2 2 2 6 0 2 Transformation Rule x y R 4 Reflect the shape below across the line y 1 Label the new coordinates and write the transformation rule 4 is done for S X 2 2 4 T 4 Q 6 Image W 4 3 X 1 3 Y 3 6 Z 2 6 Z Transformation Rule x y x y 2 S Refr the ne N

angles perpendicular lines parallel lines and line segments can develop definitions of reflections in terms of Standard G CO A 4 EXPLORE Exploring Reflections Read Explore in your textbook Lesson 2 2 and complete the following Show all your work Using tracing paper complete steps Instead of using quadrilateral ABCD from your book use quadrilateral and B FGHI to the right Label appropriately from your textbook attach tracing paper here LAL Math Resources http Bit ly L4LMath H C Draw segments to connect each vertex of quadrilateral FGHI with its image Use a protractor to measure the angle formed by each comment and ling What do you notice

5 Draw the image when ABCD is translated along 4 6 8 6 4 4 2 What is the coordinate for C 0000 C 2 2 0 A 0 2 4 B 2 B C 4 A 7 Triangle ABC is translated to A B C Which of the 8 Quadrilateral QRST is translated to Q R S T following represents the rule for the translation D 6 B X 6 Draw the image when ABCD is translated along 6 8 A x y x 4 y 1 B x y x 3 y 1 C x y x 4 y 5 D x y x 4 y 1 What is the coordinate for B 9 6 11 7 0000 Which of the following represents the rule for the translation S D 20 2 R 2 4 T 4 B Q 6 13 8 10 S R 12 A x y x 5 y 4 B x y x 10 y 8 C x y x 6 y 2 D x y x 5 y 4 Optional Complete problems 1 3 5 7 9 15 from your textbook on separate lined paper 14 T When you are finished check the odd problems for solutions at the back of the textbook

Lesson 2 1 Checkpoint Once you have completed the above problems and checked your solutions complete the Lesson Checkpoint Complete the Lesson Reflection above by circling your current understanding of the Learning Goal below 1 Draw the preimage and image of the triangle under a translation along 1 3 Make sure to label appropriately Triangle P 1 3 Q 3 1 R 4 3 2 2 0 2 y 2 Are all translations considered a rigid motion Explain why or why not by explaining its effects on a figure s angles and line segments 2 4 X Forgot what rigid motion is Look at your Credit 1 notes

Draw the preimage and image of each triangle under a translation along 4 1 2 Triangle with coordinates P 2 1 Q 2 3 R 4 3 ty 2 2 0 2 2 Transformation Rule x y Preimage Coordinates Image

What is the measure of Angle 1 in this figure B 30 C

Find x x 6 T x 3 I x 6 u V Cross off the value of yo answer

Calculate the value of x Then calculate the measure of Angle B X A 3x 28 B 5x 52 2x 10 C

Solve for x 4x 8 B 6x A 3x 1 C

21 32 Find an equation of the plane 21 The plane through the point 1 3 and with normal vector i 4j k 22 The plane through the point 2 0 1 and perpendicular to the line x 3t y 2 t z 3 4t on panola 01 mongs 23 The plane through the point 1 1 1 and parallel to the plane 5x y z 6 24 The plane that contains the line x 1 t y 2 t z 4 3t and is parallel to the plane 5x 2y z 1 25 The plane through the points 0 1 1 1 0 1 and 1 1 0 31

39 a Find parametric equations for the line of intersection of the planes x y z 1 and x 2y 2z 1 Q b Find the angle between these planes

Write an equation for the graph given The graph represents an exponential function f with base 2 or 3 translated and or reflected f x Type an exact answer in simplified form 15 10 199 5 5 10 Ay 2 1 A 1 5 032 X Q Q y 8

8 AC 4 BC 5 D is the midpoint of AC and E is the midpoint of BC What is the area of DEC n 5 E B Cross off the value of the sum of the two digits of your answer

10 Find M Lines that look parallel are parallel L 3 M N 12 Cross off the value of your answer

1 AC 4 BC 5 D is the midpoint of AC and E is the midpoint of BC What is the area of ABC 4 Problem S E B Instructions Cross off the value of your answer

2 Find 15 K 14 Cross off the value of your answer

d In 12 15 Find the value of the variable and the measure of all the angles 12 c d 14 m 1 m 2x 5 950 x 2 7x 34 13 m 15 m 1 3y 6 2x 26 Hoff 3x 33

In 1 5 Use the given figure for which line a and line b cut by transversal line m to name each of the following 1 A pair of Corresponding Angles 2 A pair of Alternate Interior Angles 3 A pair of Same Side Interior Angles 4 A pair of Vertical Angles 5 A Linear Pair 4 1 7 8 5 m 3 2 b

10 Find the value of the variable them find the more of all ages Drawings

16 PC 12 cm F A S P B 62 D C

14 RS 43 m P R 17 TV

egion Round to the nearest 12 XY 30 ft X W 113 Z V

4 m JLK 298

7 E 68 D B 101 C m A m B

P 57 T 137 e R 41 S m40 m R mLS

T 16x 10 W 67 V

35 500

35 50

50 50

ision of depreciation Equipment with a cost of 609 300 has an estimated residual value of 65 300 has an estimated useful life of 20 years and is depreciated by the straight line method a Determine the amount of the annual depreciation b Determine the book value after 7 full years of use c Assuming that at the start of the year 8 the remaining life is estimated to be 17 years and the residual value is estimated to be 56 800 determine the depreciation expense for each of the remaining 17 years

Required information The following information applies to the questions displayed below Hudson Company reports the following contribution margin income statement Sales 10 200 units at 225 each Variable costs 10 200 units at 180 each Contribution margin Fixed costs Income HUDSON COMPANY Contribution Margin Income Statement For Year Ended December 31 HUDSON COMPANY Contribution Margin Income Statement For Year Ended December 31 Sales Variable costs Contribution margin 2 295 000 1 836 000 The marketing manager believes that increasing advertising costs by 87 000 will increase the company s sales volume to 11 600 units Prepare a contribution margin income statement for the next year assuming the company incurs the additional advertising costs 459 000 360 000 99 000 CH

Revision of depreciation A building with a cost of 2 200 000 has an estimated residual value of 85 000 has an estimated useful life of 40 years and is depreciated by the straight line method a What is the amount of the annual depreciation b What is the book value at the end of the twenty eighth year of use c If at the start of the twenty ninth year it is estimated that the remaining life is 5 years and that the residual value is 60 000 what is the depreciation expense for each of the remaining 5 years