Free Printable Unit 8 Test Review - Transformations in the Coordinate Plane

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Unit 8 Test Review - Transformations in the Coordinate Plane

Total questions: 63

Worksheet time: 45mins

Name

Class

Date

1) Triangle ABC is translated 2 units right and 1 unit down. What is the new location of point C?

(1, -7)

(1, -3)

(2, -5)

(4, -6)

2) Triangle ABC is reflected across the x-axis. What is the new location of point B?

(-4, -2)

(-4, 2)

(4, -2)

(4, 2)

3) Which translation moves a triangle 4 units to the right and 8 units up?

(x, y) --> (x + 4, y + 8)

(x, y) -->(x - 4, y + 8)

(x, y) --> (x + 8, y + 4)

(x, y) --> (x + 8, y - 4)

4) Which property changes when a figure is translated?

side lengths

angle measures

location

perimeter

5) ∆ABC is rotated 90° counterclockwise with the origin as center of rotation. Where is the image of point A?

(0, 0)

(4, -2)

(2, -4)

(2, 4)

6) Triangle ABC is rotated 90° clockwise about the origin. In what quadrant is DA'B'C', the image of the original triangle?

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

7) Which property changes when a figure is reflected across a line?

side lengths

angle measures

perimeter

orientation

8) What is the result of the transformation below?

(x, y) --> (-x, y)

reflection across the x-axis

reflection across the y-axis

90° rotation clockwise

90° rotation counterclockwise

9) A figure is translated, rotated, or reflected. Describe its image.

same shape, larger size

same shape, smaller size

same size, same shape

same size, different shape

10.

10) Triangle ABC is dilated using a scale factor of 2. What happens to its angle measures?

They double in size.

They do not change.

They become half as great.

It depends on the center of the dilation.

11.

11) A figure is dilated. Describe its image.

same size

similar

congruent

reflected

12.

12) Which transformation does not produce a congruent image?

translation

rotation

dilation

reflection

13.

13) Which transformation takes point B to (2, 4)?

reflection across the x-axis

reflection across the y-axis

90° rotation clockwise about the origin

90° rotation counterclockwise about the origin

14.

14) Which translation moves point X so that its image is on the y-axis?

(x, y) --> (x + 4, y + 8)

(x, y) --> (x - 4, y + 8)

(x, y) --> (x + 8, y + 4)

(x, y) --> (x + 8, y - 4)

15.

15) Triangle XYZ is reflected across the y-axis. What are the endpoints of segment Y'Z'?

(-2, -3), (-2, -3)

(-2, 3), (-2, -3)

(2, 3), (2, -3)

(2, 3), (-2, -3)

16.

16) The transformation below is applied to DXYZ. What are the coordinates of point X'?

(-4, 1)

(-2, 0.5)

(0.5, -2)

(4, -1)

17.

17) A polygon is translated 7 units to the right and 2 units down. Which translation returns it to its original location?

(x, y) --> (x - 7, y + 2)

(x, y) --> (x - 2, y + 7)

(x, y) --> (x + 2, y - 7)

(x, y) --> (x + 7, y - 2)

18.

18) A quadrilateral with vertices at H(-5, 8), J(0, 10), K(4, 0), and L(-8, -3) is reflected across the y-axis. Which point does not change location?

point H

point J

point K

point L

19.

19a. What is the scale factor of this dilation?

1/3

3/2

2/3

20.

19b. What are the coordinates of the center of the dilation?

(0, 0)

(3, 0)

(3, 6)

(3, 9)

21.

20a. Which dilation centered at the origin would create line segment X'Y' with endpoints at (12, 4.5) and (12, -6)?

(x, y) --> (0.5x, 0.5y)

(x, y) --> (1.5x, 1.5y)

(x, y) --> (2.5x, 2.5y)

(x, y) --> (3.5x, 3.5y)

22.

20b. What if instead Quadrilateral WXYZ is dilated by a scale factor of 3.5 with the origin as its center. What are the coordinates of the vertices of Quadrilateral W'X'Y'Z'?

(3, 12), (24, 9), (24, -12), (9, -15)

(3.5, 12), (28, 9), (28.5, -12), (10.5, -15)

(3.5, 14), (28, 10.5), (28, -14), (10.5, -17.5)

(3, 14), (24, 10.5), (24, -14), (9, -17.5)

23.

21) A triangular sign was moved. The new location of the sign is represented by the shaded triangle. Which transformation could have been used to move the sign to the new location?

Reflection across side BC and reflections across side AC.

Reflection across side BC and translation 4 units right

Translation 4 units right and translation 4 units down

Rotation 180 degrees clockwise about C and translation 4 units right

24.

22) In the grid shown below, rectangle ABCD represents the location of a pool at a city park. Jackson swims in a straight line from corner A to corner C of the swimming pool. What is the distance, in meters, Jackson swims?

$\sqrt{22}$

$\sqrt{65}$

25.

23) Which of these triangles are reflections of triangle ABC?

Triangle DEF is a reflection of triangle ABC.

Triangle DEF and triangle GHJ are reflections of triangle ABC.

Triangle KMN is a reflection of triangle ABC.

Triangle DEF, triangle GHJ, and triangle KMN are reflections of triangle ABC.

26.

24) Describe in words how to map triangle ABC to its image triangle A'B'C'. Which words below describe the mapping?

Triangle A'B'C' is the image of triangle ABC after a reflection across the y-axis.

Triangle A'B'C' is the image of triangle ABC after a reflection across the line x=-2.

Triangle A'B'C' is the image of triangle ABC after a reflection across the x-axis.

Triangle A'B'C' is the image of triangle ABC translated 2 units horizontally.

27.

27) Which of the following sentences describes the transformation of the object below?

Shift the arrow down 7 units and to the right 3 units, and then reflect across the y-axis

Shift the arrow down 1 unit and to the right 1 unit, and then reflect across the x-axis.

Reflect the arrow across the x-axis, and then shift up 1 unit and to the right 1 unit.

Reflect the arrow across the y-axis, and then shift down 7 units and to the right 3 units.

28.

28) Which of the following sentences describes the transformation of the object below?

a reflection across the x-axis, followed by a translation of 4 units down, and then a dilation by a scale factor of 0.5.

a translation of 4 units down, followed by a reflection across the x-axis, and then a dilation by a scale factor of 2

a 180 degree rotation about the origin, and then a dilation by a scale factor of 0.5

a dilation by a scale factor of 2, and then a rotation about the origin

29.

31) Which coordinate plane shows that the shaded polygon is the image of the unshaded polygon after a 90 degree counterclockwise rotation about the origin?

30.

32) In the figure shown, triangle PQR is transformed to create triangle P'Q'R'. Point S will be transformed the same way as triangle PQR. Which sentence could describe how point S will be transformed?

. Point S will be translated to (6,0) and then rotated to (0,6).

Point S will be translated to (6,0) and then rotated to (0,-6).

Point S will be translated to (4,3) and then reflected to (-4, 3).

Point S will be translated to (4,3) and then reflected to (4, -3).

31.

34) Triangle LNR is graphed on a coordinate grid shown below. A translation 3 units right and 2 units down, followed by a dilation centered at the origin with a scale factor of 2, is performed on triangle LNR to create triangle L'N'R'. Which statement about side L'N' of triangle L'N'R' is true?

Because vertex L' is located at (-4,4) and vertex N' is located at (2, -4), the length of side L'N' is 10 units.

Because vertex L' is located at (-2,6) and vertex N' is located at (4,-2), the length of side L'N' is 10 units.

Because vertex L' is located at (-4,4) and vertex N' is located at (2, -4), the length of side L'N' is 12 units.

Because vertex L' is located at (-2,6) and vertex N' is located at (4,-2), the length of side L'N' is 12 units.

32.

35) Which graph shows only a rotation of 180 degrees about the origin of square JKLM to square J'K'L'M'?

33.

36) Jenna and Hunter are packing boxes.

The equation y=7x+50 represents the number of boxes Jenna packed in x hours.

The table shows the number of boxes Hunter packed in x hours.

Which of the following is true?

Hunter packed more boxes per hour than Jenna.

Jenna and Hunter packed the same number of boxes per hour.

There is not enough information to determine the number of boxes packed per hour.

Jenna packed more boxes per hour than Hunter.

34.

37) Avery drew a line on the coordinate plane that passes through the points (-1, 12) and (3,-4). What equation below represents the line that Avery drew? (You must show work.)

$y=-4x+4$

$y=-\frac{1}{4}x+8$

$y=-8x+4$

$y=-4x+8$

35.

38) In the prism below, the shortest distance between vertex A and vertex G is 7.34 feet, and the shortest distance from vertex E and vertex G is 6.04 feet. What is the approximate length of AE? (You must show work.)

1.3 feet

5.08 feet

17.39 feet

4.17 feet

36.

39a) The scatter plot suggests a linear association among the data. Two points that lie on the trend line drawn for the data are (3, 41) and (5, 31). Find the slope, m, of the trend line.

(a)

37.

39b) The scatter plot suggests a linear association among the data. Two points that lie on the trend line drawn for the data are (3, 41) and (5, 31). The slope of the trend line is m = -5. Find the y-intercept, b, of the trend line.

(a)

38.

40) The data table shows the price of a certain stock on the first day of several months in one year. The equation of the trend line shown is y=0.4x+12, where x represents the month and y represents the price of the stock. In which month was the price of the stock about $16.40?

(a)

39.

41a) In a recent survey, eighty people were asked, "Do you exercise regularly?" The frequency table shows the results of the survey. What percent of those surveyed are men who exercise regularly (joint relative frequency)? (Round to the nearest tenth of a percent, if necessary.)

(a)

40.

41b) In a recent survey, eighty people were asked, "Do you exercise regularly?" The frequency table shows the results of the survey. What percent of those surveyed were male (marginal relative frequency)? (Round to the nearest tenth of a percent, if necessary.)

(a)

41.

41c) In a recent survey, eighty people were asked, "Do you exercise regularly?" The frequency table shows the results of the survey. What percent of the females exercise regularly (conditional relative frequency)? (Round to the nearest tenth of a percent, if necessary.)

(a)

42.

42) Figure I is the preimage. Figure II is a translation image. Write a rule to describe the translation. The translation rule is (x,y) --> (x+___, y+___).

(x,y)-->(x+1,y-4)

(x,y)-->(x-1,y+4)

(x,y)-->(x+4,y-1)

(x,y)-->(x-4,y+1)

43.

43) Point R has coordinates (5,4). If you rotate R 90 degrees counterclockwise about the origin, (0,0), what are the coordinates of R'?

(5,4)

(4,-5)

(-5,4)

(-4,5)

44.

44a) Triangle RST has vertices R(0,0), S(6,3), and T(3,-3). Triangle R'T'S' is the image of triangle RST after a dilation with center (0,0) and scale factor 1/3. What are the coordinates of point R'?

R'(0,0)

R'(1,1)

R'(3,3)

R'(-1,1)

45.

44b) Triangle RST has vertices R(0,0), S(6,3), and T(3,-3). Triangle R'T'S' is the image of triangle RST after a dilation with center (0,0) and scale factor 1/3. What are the coordinates of point S'?

S'(0,0)

S'(2,1)

S'(3,1)

S'(1,2)

46.

44c) Triangle RST has vertices R(0,0), S(6,3), and T(3,-3). Triangle R'T'S' is the image of triangle RST after a dilation with center (0,0) and scale factor 1/3. What are the coordinates of point T'?

T'(0,0)

T'(2,1)

T'(1,-1)

T'(2,-2)

47.

51a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

48.

51b) How would you describe this rotation?

90 degrees clockwise

90 degrees counterclockwise

180 degrees

270 degrees counterclockwise

49.

51c) What is the algebraic rule for this rotation?

$(x,y)\rightarrow(-x,-y)$

$(x,y)\rightarrow(-x,y)$

$(x,y)\rightarrow(-y,x)$

$(x,y)\rightarrow(y,-x)$

50.

52a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

51.

52b) How would you describe this translation?

translation up 1 unit

translation down 1 unit

translation up 4 units

translation down 4 units

52.

52c) What is the algebraic rule for this translation?

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

(x,y)-->(x-4, y)

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

(x,y)-->(x, y-4)

53.

53a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

54.

53b) How would you describe this reflection?

reflection across the line x = 3

reflection across the line x = --3

reflection across the line y = 3

reflection across the line y = --3

55.

54a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

56.

54b) How would you describe this translation?

translation left 2 units and up 1 unit

translation right 2 units and up 1 unit

translation left 2 units and down 1 unit

translation right 2 units and down 1 unit

57.

54c) What is the algebraic rule for this translation?

$\left(x,y\right)\rightarrow\left(x+2,y-1\right)$

$\left(x,y\right)\rightarrow\left(x-2,y-1\right)$

$\left(x,y\right)\rightarrow\left(x+2,y+1\right)$

$\left(x,y\right)\rightarrow\left(x-2,y+1\right)$

58.

55a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

59.

55b) How would you describe this reflection?

reflection across the x-axis

reflection across the y-axis

reflection across the origin

reflection across the line x = 1

60.

55c) What is the algebraic rule for this rotation?

$\left(x,y\right)\rightarrow\left(-x,-y\right)$

$\left(x,y\right)\rightarrow\left(-x,y\right)$

$\left(x,y\right)\rightarrow\left(x,-y\right)$

$\left(x,y\right)\rightarrow\left(y,-x\right)$

61.

56a) What type of transformation does the picture show?

translation

reflection

rotation

dilation

62.

56b) How would you describe this rotation?

90 degrees clockwise

90 degrees counterclockwise

180 degrees

270 degrees counterclockwise

63.

56c) What is the algebraic rule for this rotation?

$(x,y)\rightarrow(-x,-y)$

$(x,y)\rightarrow(-x,y)$

$(x,y)\rightarrow(-y,x)$

$(x,y)\rightarrow(y,-x)$

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Unit 8 Test Review - Transformations in the Coordinate Plane

Total questions: 63

Worksheet time: 45mins

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