math / grade 8 / transformations review jefferson...

JEFFERSON PARISHMath / Grade 8 / Transformations review

Name _________________________________

Teacher ____________________ Period _____

1. Roman is writing a program for a newcomputer game. He needs figure A to move tofigure B. What transformation must heprogram into the game to make this move?

A. reflection about the x-axis

B. reflection about the y-axis

C. rotation 90° clockwise

D. translation (x, y) → (x, y − 2)

Use the graph below to answer question 2.

2. Which triangle is a translation of triangle 2 bythe rule (x, y) → (x + 6, y + 0)?

A. triangle 5

B. triangle 6

C. triangle 7

D. triangle 8

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JEFFERSON PARISH – Math – Grade 8 – Transformations review

3. A residential construction company laid thefoundation for a new house at the corner ofPark Street and Second Avenue. Righttrapezoid HOME shows the location of thefoundation in the diagram below.

The company plans to lay another foundation,H′O′M′E′, across Park Street so that it is areflection of HOME. Which of the followingwill be true if the foundation for H′O′M′E′ islaid?

A. H′ will be a right angle.

B. O′ will be an obtuse angle.

C. M′ will be a straight angle.

D. E′ will be an acute angle.

Use the information below to answer questions 4and 5.

Walt has an octagonal carpet near the corner of hisliving room, as shown on the coordinate planebelow.

4. If Walt translates the carpet according to therule (x, y) → (x – 2, y – 2), how will its anglemeasures be affected?

A. They will be halved.

B. They will be doubled.

C. They will be the same.

D. They will be decreased by 2.

5. If Walt translates the carpet according to therule (x, y) → (x – 2, y – 2), how will its sidesbe affected?

A. The longer sides will remain parallel.

B. The shorter sides will remainperpendicular.

C. The horizontal and vertical sides willbecome longer.

D. The horizontal and vertical sides willbecome shorter.

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6. The equations below show the equations fortwo different lines.

y = 15 x − 4

y = 15 x + 4

If both lines are rotated 90° counterclockwiseabout the origin to form two new lines, whichof the following correctly describes therelationship between the two new lines?

A. collinear

B. parallel

C. perpendicular

D. skew

7. The shaded figure on the coordinate planebelow represents the former location of abaseball park. Rotating the old location 180°about the origin shows the location of the newpark that replaced it.

Which term best describes the relationshipbetween the old park and the new park?

A. congruent

B. parallel

C. perpendicular

D. similar

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8. The white figure on the coordinate planebelow represents where Ron parked his truckyesterday. The shaded figure shows where heparked it today.

Which of the following does not describe apossible transformation between the twofigures?

A. dilation

B. reflection

C. rotation

D. translation

9. Use the graph below to solve the problem.

Which sequence correctly describes thetransformation from ABCD to A′B′C′D′?

A. Translate (x, y) → (x + 10, y + 1).Reflect over the x-axis.

B. Translate (x, y) → (x – 1, y + 1).Rotate 180° about the origin.

C. Translate (x, y) → (x + 1, y – 1).Reflect over the x-axis and y-axis.

D. Translate (x, y) → (x – 1, y – 6).Rotate 90° counterclockwise about theorigin.

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10. The coordinates of a triangle are (3, – 1),(7, – 2), and (1, – 4). What are the coordinatesof the image of this triangle after thetransformation up 2, left 6?

A. (– 6, 2), (– 8, – 1), (– 2, 1)

B. (– 3, 1), (1, 0), (– 5, – 2)

C. (– 1, 2), (1, 5), (5, 4)

D. (1, – 3), (0, 1), (– 2, – 5)

11. Δ ABC has vertices A ( − 2, 3), B (4,1), andC (2, − 3). What are the coordinates of itsimage ΔA'B'C' after reflecting it over the x-axis?

A. A'( − 2, − 3), B'(4, − 1), C'(2, 3)

B. A'(2, 3), B'( − 4, 1), C'( − 2, − 3)

C. A'(2, − 3), B'( − 4, − 1), C'( − 2, 3)

D. A'( − 2, − 3), B'(4, − 1), C'(2, − 3)

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12. Lily transformed ∆ABC below. The result isshown in dotted lines. Which of the followingdescribes Lily's transformation?

A. rotated 90° clockwise about the origin

B. rotated 90° counterclockwise about theorigin

C. rotated 180° about the origin

D. reflected across the x-axis

Use the graph below to answer question 13.

13. How was ABCD transformed to A′B′C′D′?

A. Reflect over the x-axis and dilate by ascale factor of 2 relative to (0, 0).

B. Reflect over the x-axis and dilate by ascale factor of 1

2 relative to (0, 0).

C. Rotate 90° counterclockwise and dilate bya scale factor of 2 relative to (0, 0).

D. Rotate 90° counterclockwise and dilate bya scale factor of 1

2 relative to (0, 0).

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Use the information below to answer question14.

A thought bubble from a comic strip is drawn onthe coordinate plane below.

14. Which transformation can be used to turnfigure A into figure B?

A. Dilate by a factor of 3 relative to theorigin. Translate 1 unit to the left.

B. Dilate by a factor of 3 relative to theorigin. Translate 1 unit to the right.

C. Dilate by a factor of 13 relative to the

origin. Translate 1 unit to the left.

D. Dilate by a factor of 13 relative to the

origin. Translate 1 unit to the right.

15. Jonesboro Police Department is consideringre-routing traffic at the intersections shownbelow where more than the average number ofaccidents are reported. What is the geometricdescription of the relationship between Ә Aand Ә B?

A. alternate exterior angles

B. alternate interior angles

C. corresponding angles

D. linear pair

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16. Below is a map of Miles’ neighborhood. Theavenues are parallel, and Miles walks on a pathacross them to get to the park. If Ә 3 is 50°,what is the measure of Ә 4?

A. 40°

B. 50°

C. 130°

D. 150°

17. Suppose two parallel lines are cut by atransversal and angles 1 and 5 are alternateexterior angles. If m Ә 5 = 84°, what ism Ә 1?

A. m Ә 1 = 6°

B. m Ә 1 = 84°

C. m Ә 1 = 96°

D. m Ә 1 = 174°

18. Given that r||s and t is a transversal, which ofthe following lists shows all angles that arecongruent to Ә 1?

A. Ә 1 ӽ Ә 3

B. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә 5

C. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә 5, Ә 1 ӽ Ә 7

D. Ә 1 ӽ Ә 3, Ә 1 ӽ Ә 7

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19. Alan laid a wooden board across a smallstream in order to cross it. The diagram belowshows the board, the stream, and the distancebetween the stream’s banks where the boardintersects the banks.

Which of the following would be sufficient toprove that triangle BGH is similar to triangleJDC?

A. AE ӝ FK

B. BH ӝ CJ

C. ә ABG ӽ ә DJK

D. ә GBH ӽ ә DJC

20. Line segment AC and line segment ED areparallel.

Which statement could be used to argue that∆ABC and ∆EBD are similar?

A. BC and AB are equal.

B. DB + DC = CB

C. ә 1 = ә 3, ә 2 = ә 4

D. ә 1 = ә 2, ә 3 = ә 4

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JEFFERSON PARISHOpen-Response / Grade 8 / Transformations review

Name _________________________________

Teacher ____________________ Period _____

MATH OPEN-RESPONSE ITEM A

A. Randa is designing a stained-glass window. The grid provided in your Student Answer Document showsRanda's first design, labeled F1.

1. Rotate F1 clockwise 90° about point D, resulting in Figure 2. Label each vertex with its correspondingletter. Label this figure F2.

2. Reflect F2 over the x-axis, resulting in Figure 3. Label each vertex with its corresponding letter. Labelthis figure F3.

3. Translate F3 to the right 8 units and up 11 units, resulting in Figure 4. Label each vertex with itscorresponding letter. Label this figure F4.

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JEFFERSON PARISHStudent Answer Document / Grade 8 / Transformations review

Name _________________________________

Teacher ____________________ Period _____

11

A

MATH OPEN-RESPONSE ITEM A (8.G.1A, 8.G.1B, 8.G.1C)

A. Randa is designing a stained-glass window. The grid provided in your Student Answer Document shows Randa's first design,labeled F1.

1. Rotate F1 clockwise 90° about point D, resulting in Figure 2. Label each vertex with its corresponding letter. Label thisfigure F2.

2. Reflect F2 over the x-axis, resulting in Figure 3. Label each vertex with its corresponding letter. Label this figure F3.

3. Translate F3 to the right 8 units and up 11 units, resulting in Figure 4. Label each vertex with its corresponding letter. Labelthis figure F4.

RUBRIC FOR MATH OPEN-RESPONSE ITEM A (8.G.1A, 8.G.1B, 8.G.1C)

Score Description

4 The student earns 6 points. The response contains no incorrect work.

3 The student earns 4 – 5 points.

2 The student earns 2 – 3 points.

1 The student earns 1 point or some minimal understanding is shown.

0 The student earns 0 points. No understanding is shown.

B Blank – No Response. (No attempt to answer the item. Score of “0” assigned for the item.)

Solution and Scoring

Part Points1 2 points possible

1 point: Student correctly drew Figure 2.AND 1 point: Student correctly labeled Figure 2.

2 2 points possible (Based on student's answer from Part 1.)1 point: Student correctly drew Figure 3.AND 1 point: Student correctly labeled Figure 3.

3 2 points possible (Based on student's answer from Part 2.)1 point: Student correctly drew Figure 4.AND 1 point: Student correctly labeled Figure 4. Give credit for the following or equivalent graph.

Note: Hash marks are not required on F2, F3, or F4 to earn a score of 6.

JEFFERSON PARISHMath / Grade 8 / Transformations reviewAnswer Key and Alignment

Answer Source SLE CC-Standard1. A TLI G.9.8.2b 8.G.1a2. B TLI G.9.8.2a 8.G.1a3. D TLI 8.G.1b4. C TLI 8.G.1b5. A TLI 8.G.1c6. B TLI 8.G.1c7. A TLI 8.G.28. A TLI 8.G.29. B TLI 8.G.210. B TLI G.9.8.2a 8.G.311. A TLI G.9.8.2b 8.G.312. B TLI G.9.8.2c 8.G.313. C TLI 8.G.414. C TLI 8.G.415. B TLI G.8.7.3c 8.G.5(A)16. C TLI G.8.7.3c 8.G.5(A)17. B TLI G.8.7.3c 8.G.5(B)18. C TLI G.8.7.3c 8.G.5(B)19. D TLI 8.G.5(C)20. D TLI 8.G.5(C)

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