GEOMETRY

The University of the State of New York

REGENTS HIGH SCHOOL EXAMINATION

GEOMETRY Thursday, January 24, 2013- 9:15a.m. to 12:15 p.m., only

Student

School Name: ______________________________________________________ __

The possession or use of any communications device is strictly prohibited when taking this examination. If you have or use any communications device, no matter how briefly, your examination will he invalidated and no score will be 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 the proctor for completing the student information on your answer sheet.

This examination has four parts, with a total of 38 questions. You must answer all questions in this examination. Record your answers to the Part I multiple-choice questions on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV directly in this hooklet. All work should be written in pen, except for graphs and drawings, which should be done in pencil. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.

The formulas that you may need to answer some questions in this examination are found at the end 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, hut you may use the blank spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided at the end of this hooklet for any question for which graphing may be helpful but is not required. You may remove this sheet from this hooklet. 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 of the answer sheet, indicating that you had no unlawful knowledge of the questions or answers prior to the examination and that you have neither given nor received assistance in answering any of the questions during the examination. Your answer sheet cannot he accepted if you fail to sign this declaration.

Notice ...

A graphing calculator, a straightedge (ruler), and a compass must be available for you to use while taking this examination.

DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.

AtU.311\lO 3 8

Part I

Answer all28 questions in this part. Each correct answer will receive 2 credits. No partial credit will be allowed. For each statement or question, choose the word or expression that, of those given, best completes the statement or answers the question. Record your answers on your separate answer sheet. [56]

I If !:J.MNP :::: l:J. VWX and PM is the shortest side of !:J.MNP, what is the shortest side of l:J. VWX?

(1) XV (2) wx

(3) vw (4) NP

2 In circle 0 shown in the diagram below, chords AB and CD are parallel.

A

If mAE = 104 and mCD = 168, what is mJID?

(1) 38

(2) 44

Geometry- January '13

(3) 88

(4) 96

D

[2]

Use this space for computations.

3 As shown in the diagram below, CD is a median of 6.ABC.

c

~ A D B

Which statement is always true?

(1) AD::::: DB

(2) AC::::: AD

(3) LACD::::: LCDB

(4) LBCD::::: LACD

4 In the diagram below, under which transformation is 6.A 'B 'C' the image of 6.ABC?

y

X

(3)

(4) (x,y)--+ (x-2,y)

Geometry- January '13 [3]

Use this space for computations.

[OVER]

nn>t:>rt:>r of 0 whose center has 5 Line segment AB is a coordinates (6,8). What are the coordinates of point A are ( 4,2)'?

coordinates of point B if the

(10,10)

6 Plane )I and plane CB are two distinct planes that are both perpendicular to line e. ·which statement about planes )I and CB is true?

(1) Planes )I and CB have a common edge, which forms a line.

Planes )I and CB are perpendicular to each other.

Planes and CB intersect each other at exactly one point.

Planes )I and CB are parallel to each other.

7 Triangle ABC is similar to triangle DEF. The lengths of the sides of ~ABC are 5, 8, and 11. What is length of the shortest side of ~DEF if its perimeter is 60?

10

Geometry- January '13

20 27 .. 5

Use this space for computations.

8 In diagram below of right triangle ABC, CD is drawn to hypotenuse AB.

c

A 3 D 12 B

If AD = 3 and DB =

6

what is the length of altitude CD?

3

9 The below shows the construction of an equilateral

\Vhich statement

LA+ + LC = 180

mLA = mLB = mLC

AB AC = BC

AB + BC >AC

10 \Vhat is the slope of the line perpendicular to the line by the equation + 4y = 12?

-2 l 2

2 1 2

Geometry- January '13

Use this space for computations.

[OVER]

II Triangle ABC is shown in the diagram below.

A

If DE joins the midpoints of ADC and AEB, which statement is not tme?

DE= ~ CB

DEI!CB

DE = DC CB

L:.ABC ~ L:.AED

I2 The equations + y2 = 25 andy = 5 are graphed on a set of axes. vVhat is the solution of this system?

(0,0)

(2) (5,0)

(0,5)

(5,5)

I3 Square ABCD has vertices A( B(4, -1), C(2,.5), and D( -4,3). What is the length of a of the square?

1) 2/5

(2) 2.Ji0

Geometry- January '13

Use this space for computations.

--14 The diagram below shows .6ABD, with ABC , BE J.. AD, and LEBD :::: LCBD.

A

If mLABE = 52, what is mLD?

(1) 26

(2) 38

B

.52

64

0

15 As shown in the diagram below, FD and CB intersect at point A and ET is perpendicular to both FD and CB at A.

E

T

\Vhich statement is not true?

(1) ET is perpendicular to plane BAD.

(2) ET is perpendicular to plane FAB.

(3) ET is perpendicular to plane CAD.

(4) ET is perpendicular to plane BAT.

Geometry- January '13 [7]

Use this space for computations.

[OVER]

16 \Vhich set of numbers could not represent the lengths of the sides of a right hiangle?

{3,4,5}

{8,15,17}

17 How many points are .5 units from a line and also equidistant from two points on the line?

(1) l

2

3

0

18 The equation of a circle is - 2)2 + (y + 5)2 = 32. What are the coordinates of center of this circle and the length of its radius?

(1) ( 2,5) and 16

-5) and 16

( -2,5) and 4J2 (2, -,5) and 4J2

19 The equation of a line is y = 2 + 5. What is an equation of the

line that is perpendicular to the given line and that passes through the point

2 2 (1) y = 3x- 3

l'f = l_x- 4 . 2'

Geometry January '13 [8]

Use this space for computations.

20 Consider the relationship between the two statements below.

If .J16 + 9 4 + 3, then 5 # 4 + 3.

If .Jl6 + 9 = 4 + 3, then 5 = 4 + 3.

These statements are

( 1) inverses

(2) converses

( 3) contrapositives

(4) biconditionals

21 In the diagram of trapezoid ABCD below, AB II DC, AD:::::: BC, mLA = 4x + 20, and mLC = 3x - 15.

What is mLD?

(1) 25 (2) 35

Geometry- January '13

A

(4x + 20t

(3) 60

(4) 90

B

[9}

Use this space for computations.

[OVER}

22 In circleR shown below, diameter DE is perpendicular to chord ST at point L.

D

E

Which statement is not always tme?

(3) RL :::: LE (I) SL :::: TL

(2) RS =DR (4) (DL)(LE) = (SL)(LT)

23 Which equation represents circle A shown in the diagram below?

y

X

(I) (x - 4)2 + (y - I)2 = 3 (3) (x - 4)2 + (y - I)2 = 9

(2) (x + 4)2 + (y + I)2 = 3 (4) (x + 4)2 + (y + 1)2 = 9

Geometry -January '13 [ 10]

Use this space for computations.

24 Which equation represents a line that is parallel to the line whose equation is 3x - 2y = 7?

3 y = -2x + 5

3 y = 2x- 5

2 (2) y= -3x+4

9 y = ~ -4

25 In the diagram below of circle 0, PAC and PBD are secants.

-- -If mCD = 70 and mAB = 20, what is the ""'"'r"""' measure of LP?

(1) 25

(2) 35

45 50

26 The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have?

(1) 5 3 (2) 6 (4) 4

Geometry -January '13 [11}

Use this space for computations.

[OVER]

27 As shmv:n in the diagram of rectangle ABCD below, diagonals AC

and BD at

If AE = x + 2 and BD =

(1) 6 10

28 If of f:o.ABC are f:o.ABC is classified as

Geometry- January '13

-16, then the length of AC is

12

B( and

equilateral

(12]

then

Use this space for computations.

Part II

Answer all 6 questions in this part. Each correct answer will receive 2 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil. [ 12)

29 After the transformation ry = x, the image of /:;,.ABC is /:;,.A' B 'C '. AB 2x+ and A'B' = 9x - 8, find the value of x.

Geometry - January '13 [13} [OVER1

30 In the diagram below, circles A and B are tangent at point C and AB is drawn. Sketch all common tangent lines.

Geometry- January '13 [14]

31 On the set of axes below, graph the locus of points 4 units from (0,1) and the locus of points 3 units from the origin. Label with an X any points that satisfy both conditions.

y

Geometry -January '13 [15] [OVER]

32 Write an equation of a circle whose center is ( -3,2) and whose diameter is 10.

Geometry- January '13 [16]

33 Using a compass and straightedge, construct a line perpendicular to line f through point P. (Leave all construction marks.]

Geometry- January '13 [17] [OVER]

34 Write an equation of the line that is the perpendicular bisector of the line segment having endpoints (3, -1) and (3,5). [The use of the grid below is optional.]

y

Geometry -January •13 [18]

Part III

Answer all 3 questions in this part. Each correct answer will receive 4 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. For all questions in this part, a correct numerical answer with no work shown will receive only 1 credit. All answers should be written in pen, except for graphs and drawings, which should be done in pencil.

35 A right circular cylinder with a height of 5 em has a base with a diameter of 6 ern. Find the lateral area of the cylinder to nearest hundredth of a square centimeter·.

Find the volume of the cylinder to the nearest hundredth of a cubic centimeter.

Geometry- January '13 [19] [OVER]

36 Triangle ABC has A(.5,1), B(

State and label the coordinates of composite transformation T1 _1 o D2.

Geometry- January '13

1,

of D.A"B"C", the image of !:::.ABC, following use of the set of axes below is optional.]

y

[20]

37 In l.:.ABC, mLA = + 12, mLB = llx + 5, and mLC 13x 17. Determine the longest side of l.:.ABC.

Geometry- January '13 [21] IOVEH

Part IV

Answer the question in this part. A correct answer will receive 6 credits. Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc. A correct numerical answer with no work shown will receive only 1 credit. The answer should be written in pen, except for graphs and drawings, which should be done in pencil.

38 The diagram below shows rectangle ABCD with points E and F on side AB. Segments CE and DF intersect at G, and LADG :::::: LBCG.

Prove that AE ::::.BF.

B

Geometry- January '13 [22]

Raw Scale Raw Scale Raw Scale Raw ScaleScore Score Score Score Score Score Score Score

86 100 64 80 42 66 20 4285 98 63 79 41 66 19 4184 97 62 79 40 65 18 3983 95 61 78 39 64 17 3782 94 60 77 38 63 16 3581 93 59 77 37 62 15 3480 92 58 76 36 61 14 3279 91 57 76 35 60 13 3078 90 56 75 34 59 12 2877 89 55 75 33 58 11 2676 88 54 74 32 57 10 2475 87 53 74 31 56 9 2274 86 52 73 30 55 8 1973 86 51 72 29 54 7 1772 85 50 72 28 53 6 1571 84 49 71 27 51 5 1370 83 48 71 26 50 4 1069 83 47 70 25 49 3 868 82 46 69 24 48 2 567 81 45 68 23 46 1 266 81 44 68 22 45 0 065 80 43 67 21 43

Schools are not permitted to rescore any of the open-ended questions on this exam after each question hasbeen rated once, regardless of the final exam score. Schools are required to ensure that the raw scores havebeen added correctly and that the resulting scale score has been determined accurately.

Because scale scores corresponding to raw scores in the conversion chart change from one administration toanother, it is crucial that for each administration the conversion chart provided for that administration be used todetermine the student’s final score. The chart above is usable only for this administration of the Regents Examinationin Geometry.

The State Education Department / The University of the State of New York

Regents Examination in Geometry – January 2013

Chart for Converting Total Test Raw Scores to Final Examination Scores (Scale Scores)

To determine the student’s final examination score, find the student’s total test raw score in the column labeled “RawScore” and then locate the scale score that corresponds to that raw score. The scale score is the student’s finalexamination score. Enter this score in the space labeled “Scale Score” on the student’s answer sheet.

Geometry Conversion Chart - January '13 1 of 1