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GEOMETRYThe University of the State of New YorkREGENTS HIGH SCHOOL EXAMINATIONGEOMETRYWednesday, January 23, 2019 - 9:15 a.m. to 12:15 p.m., onlyStudent Name:/YI---"·---·"--"'., ('. - ) ).&J. )j/ {VJ . fl :P . · .School Name:The possession or use of any communications device is strictly prohibited whentaking this examination. If you have or use any communications device, no matter howbriefly, your examination will he invalidated and no score will he calculated for you.Print your name and the name of your school on the lines above.A separate answer sheet for Part I has been provided to you. Follow the instructions from theproctor for completing the student information on your answer sheet.This examination has four parts, with a total of 35 questions. You must answer all questionsin this examination. Record your answers to the Part I multiple-choice questions on the separateanswer sheet. Write your answers to the questions in Parts II, III, and IV directly in this booklet.All work should be written in pen, except for graphs and drawings, which should be done inpencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams,graphs, charts, etc. Utilize the information provided for each question to determine your answer.Note that diagrams are not necessarily drawn to scale.The formulas that you may need to answer some questions in this examination are found at theend of the examination. This sheet is perforated so you may remove it from this booklet.Scrap paper is not permitted for any part of this examination, but you may use the blank spacesin this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of thisbooklet for any question for which graphing may be helpful but is not required. You may removethis sheet from this booklet. Any work done on this sheet of scrap graph paper will not be scored.When you have completed the examination, you must sign the statement printed at the end ofthe answer sheet, indicating that you had no unlawful knowledge of the questions or answers priorto the examination and that you have neither given nor received assistance in answering any of thequestions during the examination. Your answer sheet cannot be accepted if you fail to sign thisdeclaration.Notice .A graphing calculator, a straightedge (ruler), and a compass must he available for youto use while taking this examination.DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.Atl.l3V\1038

Part IAnswer all 24 questions in this part. Each correct answer will receive 2 credits. No partialcredit will be allowed. Utilize the information provided for each question to determine youranswer. Note that diagrams are not necessarily drawn to scale. For each statement or question,choose the word or expression that, of those given, best completes the statement or answersthe question. Record your answers on your separate answer sheet. [48]1 After a dilation with center (0,0), the image of DB is D'B'.If DB 4.5 and D' B' 18, the scale factor of this dilation is(1) -51l.'l (3) [email protected](2) 511""2 In the diagram below, 6.ABC with sides of 13, 15, and 16, is mappedonto 6.DEF after a cloc se rotation of 90 about point P.--EcFBD pIf DE 2x - 1, what is the value of x?(l) 7(2) 7.5tt).sx.- ,I')-x-,){ jGeometry - Jan. '19l-6lf? c;[2]Use this space forcomputations.

3 On the set of axes below, 6ABC has vertices at A(-2,0), B(2, -4),C(4,2), and 6DEF has vertices at D(4,0), E(-4,8), F(-8, -4).Use this space forcomputations.y· EIJ"IIIJjI--IF """,,,,,,,. .,,,,,,,,. . ,,,,.Af\,, .,,,,-- .,,,,,,,,. ,jIL- ,.,,- ---"",,,,,- )( .-J ,,,,. ,,,,,-'("'"' """ "" "',,,,,,.,.,,.,.,,,.,,,,,,,, .,,,,. IJ"' "I I,,.--,-,A) (-t, ()) 8 {4, ) c'( 1J l lf. o) El-4, ) f" -l )1IIJID-- xII",.'\'--c . ( .,t : * Which sequence of transformations will map 6ABC onto 6DEF?( 1) a dilation of 6AB C by a scale factor of 2 centered at point A(2) a dilation of 6ABC by a scale factor of ; centered at point [email protected] a dilation of L.ABC by a scale factor of 2 centered at the origin,followed by a rotation of 180 about the origin(4) a dilation of 6ABC by as ale factor of centered at theorigin, followed by a rotation of 180 about the originGeometry - Jan. '19[3][OVER]

4 The figure below shows a rhombus with noncongruent diagonals.Which transformation would not carry this rhombus onto itself?( 1) a reflection over the shorter diagonal(2) a reflection over the longer [email protected]!: . clockwiserotation of 90 about the intersection of thediagonals(4) a counterclockwise rotation of 180 about the intersection of thediagonals5 In the diagram below of circle 0, points K, A, T, I, and E are on the circle, 6.KAE and 6.ITE are drawn, KE --- EI, and LEKA --- LEIT.Which statement about 6.KAE and 6.ITE is always true?(1) They are neither congruent nor similar.(2) They are similar but not congruent. They are right triangles.\:.9' They are congruent. AA )Geometry - Jan. '19[4]Use this space forcomputations.

6 In right triangle ABC shown below, point D is on AB and point E isUse this space forcomputations.on CB such that AC 11 DE.A17/ ,,. ))- )----- --- BcIf AB 7E15, BC 12, and EC 7, what is the length of BD? 8.75(3) 5 6.25(4) 47 In rhombus VENU, diagonals VN and EU intersect at S.If VN 12 and EU 16, what is the perimeter of the rhombus? 80(3) [email protected])40(4) 10. . fV,··o··:;,11.10Geometry- Jan. '19[5][OVER]

8 Given right triangle ABC with a right angle at C, mLB 61 .Given right triangle RST with a right angle at T, mLR 29 .A8RcTsWhich proportion in relation to L.ABC and L.RST is not correct?G A B RTRs(2 ) BCSTAc j\G(3)Ls- P.,iABRS(4 )BCACsTRTABRSRTAC9 A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of thetent are 9 ft tall and the top forms a square pyramid with a height of3 ft.i - - - - - 8 ft1.- 8 ft What is the volume, in cubic feet, of space the tent occupies? 256(3) 672c;Y640(4) 768Geometry - Jan. '19[6]Use this space forcomputations.

10 In the diagram below of right triangle KM.I, altitude IG is drawn toUse this space forcomputations.hypotenuse KM.Jl! 9tf1KqG){M 1l16rxy }- /b, ) y: J-DIf KG 9 and I G 12, the length of IM is(1) [email protected](2) 16(4) 2511 Which three-dimensional figure will result when a rectangle 6 incheslong and 5 inches wide is continuously rotated about the longer side?(1) a rectangular prism with a length of 6 inches, width of 6 inches,and height of 5 inches(2) a rectangular prism with a length of 6 inches, width of 5 inches, and height of 5 inches acylinder with a radius of 5 inches and a height of 6 inches(4) a cylinder with a radius of 6 inches and a height of 5 inches12 Which statement about parallelograms is always true?The diagonals are congruent.The diagonals bisect each other.) The diagonals are perpendicular.(4) The diagonals bisect their respective angles.Geometry - Jan. '19[7][OVER]

13 From a point on the ground one-half mile from the base of a historicmonument, the angle of elevation to its top is 11.87 . To the nearestfoot, what is the height of the [email protected] i Use this space forcomputations. f av.I l 7 {o. ;)(f)n X' 5 14 The area of a sector of a circle with a radius measuring 15 cm is751t cm2 What is the measure of the central angle that forms thesector?· 72 (3) 144 120 (4) 180 (Is) ;rt 7 fx/- JH)15 Point M divides AB so that AM:MB 1:2. If A has coordinatesx,-3) and B has coordinates (8,9), the coordinates of Mare (2,1)(2) ( ,o)(3) (5,5)(4)( 2 ,8)- / /- J.( 'i. -IL3 .I . I r) ] X 3 I- (q - 3)Geometry - Jan. '19 -3 llJ }[8]y

16 In the diagram below of triangle ABC, AC is extended throughUse this space forcomputations.point C to point D, and BE is drawn to AC.BWhich equation is always true?(1) mLl mL3 mL2(2) mL5 mL3 - mL2 mL3 - mL2(0)/mL 7 mL3 mL2 mL6t yvl ) Dve/l'j17 In the diagram below of right triangle ABC, ACL 8, and AB 17.B17cµ'-ffA8At JWhich equation would determine the value of angle A?. A(1) sm8 l7(2) tanA Geometry - Jan. '191 (3) cos A15 [email protected] ;[9][OVER]

18 Francisco needs the three pieces of glass shown below to completea stained glass window. The shapes, two triangles and a trapezoid,are measured in inches.Q6121259205Glass can be purchased in rectangular sheets that are 12 inches wide.What is the minimum length of a sheet of glass, in inches, thatFrancisco must purchase in order to have enough to complete the dow?\gj 20(3) 29(2) 25(4) 3419 In the diagram of quadrilateral NAVY below, mLYNA 30 ,mLYAN 38 , mLAVY 94 , and mL VAY 46 .vy94 ''''', 46 '38 ' ',ANWhich segment has the shorte ngth?(1) AY(2) NYGeometry - Jan. '[email protected](4) VY[10]Use this space forcomputations.

20 What is an equation of a circle whose center is (1,4) and diameter [email protected](2) x22x 2x yL 8y y2 8y xL8(3)8(4) x22x 2xUse this space forcomputations y2- 8y 83fx-1Y·r { y2 8y 83'J ·r'--).) ""'11y1xl-·J--yqy., 0-f0)1--'6y1-/brl -ryj 'JS.21 On the set of axes below, 6.ABC, altitude CG, and median CM aredrawn.yWhich expression represents the area of 6.ABC?(l)(BC){Ac)2(2 ) (cc)(Bc)(3 )(cM){AB)2{;]) (cc (AB)222 In right triangle ABC, mLC 90 and AC I BC. Which trigonometric ratio is equivalent to sin [email protected](3) tanA(2) cos B(4) tan BGeometry-Jan. '19[ll][OVER]

Use this space forcomputations.23 As shown in the diagram below, the radius of a cone is 2.5 cm andits slant height is 6.5 cm.w many cubic centimeters are in the volume of the cone?12.5rc(3) 30.0rc) 13.5rc(4) 37.5rc24 What is an equation of the image of the line y dilation o! a scale factor of(I) y :x:-4(2) y 8 x - 3Geometry - Jan. '19! centered at he origin? x-4(3'.,y y 2x -6,3[12] x - 4 after a,,4c ) ; lIJM'-'1/eJrr-iSfVl p}-l){,VliCJ

Part IIAnswer all 7 questions in this part. Each correct answer will receive 2 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer.Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only I credit. All answers should hewritten in pen, except for graphs and drawings, which should he done in pencil. [14]25 Write an equation of the line that is parallel to the line whose equation is 3y 7through the point (2,6).Geometry - Jan. '19[14] 2x and passes

26 Parallelogram ABCD is adjacent to rhombus DEFG, as shown below, and FC intersects AGDatH.If mLB 118 and mLAHC 138 , determine and state mLGFH.JGeometry-Jan. '190 -( 11[15][OVER]

27 As shown in the diagram below, secants PWR and PTS are drawn to circle 0 from external point P.p,,---. If mLRPS 35 and mRS 121 , determine and state m\VT./J-l-X 1§/)-1 -x, 7vx-, lGeometry - Jan. '19[16]

28 On the set of axes below, f::::.ABC is graphed with coordinates A(-2, -1), B(3, -1), and C(-2, -4).Triangle QRS, the image of f::::.ABC, is graphed with coordinates Q(-5,2), R(-5,7), and S(-8,2).yxDescribe a sequence of transformations that would map f::::.ABC onto L::::.QRS.n( /1DoGeometry - Jan. '190T-z,,I 0[17][OVER]

29 Given points A, B, and C, use a compass and straightedge to construct point D so that ABCD isa parallelogram.[Leave all construction marks.]Geometry - Jan. '19[18]

30 On the set of axes below, 6.DEF has vertices at the coordinates D(l, -1), E(3,4), and F(4,2), andpoint G has coordinates (3,1). Owen claims the median from point E must pass through point G.Is Owen correct? Explain why.yH-t-:J\I'/ FI / Gf/""' xD.;,,,, It V. f'AL M A;dl t;y1e,tl,lh Yr-a pbi' tfof tJteo, s) ( JS,AMV :f.- Jas5 1 (bu! .fk .n;Jp(}iht.Geometry- Jan. '19[19][OVER]

31 A walking path at a local park is modeled on the grid below, where the length of each grid squareis 10 feet. The town needs to submit paperwork to pave the walking path. Determine and state,to the nearest square foot, the area of the walking path.0- - . . . . - --'- '---"- . - --'- '-------"" - - 0Geometry - Jan. '1950100[20]150

Part IIIAnswer all 3 questions in this part. Each correct answer will receive 4 credits. Clearlyindicate the necessary steps, including appropriate formula substitutions, diagrams, graphs,charts, etc. Utilize the information provided for each question to determine your answer.Note that diagrams are not necessarily drawn to scale. For all questions in this part, a correctnumerical answer with no work shown will receive only I credit. All answers should bewritten in pen, except for graphs and drawings, which should be done in pencil. [12]32 A triangle has vertices A(-2,4), B(6,2), and C(l, -1).Geometry - Jan. '19[21][OVER]

33 Theresa has a rectangular pool 30 ft long, 15 ft wide, and 4 ft deep. Theresa fills her pool usingcity water at a rate of 3.95 per 100 gallons of water.Nancy has a circular pool with a diameter of 24 ft and a depth of 4 ft. Nancy fills her pool with awater delivery service at a rate of 200 per 6000 gallons.If Theresa and Nancy both fill their pools 6 inches from the top of the pool, determine and statewho paid more to fill her pool. [1 ft 3 water 7.48 gallons]1Jz,e,y05 t1/: ( ox J Ytli-o.s)) (/' X 2-98'1 x J. 15 : t6n5Jff-3JO T' ;r;:r x 9Lt:7lf err A;;-) yl4-o. )Jr } xGeometry - Jan. '19[22]

34 As modeled in the diagram below, an access ramp starts on flat ground and ends at the beginningof the top step. Each step is 6 inches tall and 8 inches deep.BinIf the angle of elevation of the ramp is 4. 76 , determine ·and state the length of the ramp, to thenearest tenth of a foot.f S)i'n4. 70 xx 15/,/Determine and state, to the nearest tenth of a foot, the horizontal distance, d, from the bottom ofthe stairs to the bottom of the ramp.L .fl) Y}4 7h -xI. x JgGeometry - Jan. '19[23][OVER]

Part IVAnswer the question in this part. A correct answer will receive