Questions

1) Which pair of coordinates does NOT identify the corresponding point correctly?

a.) Point F

b.) Point B

c.) Point E

d.) Point A

e.) Point H

2) True or False. Points C and E lie in Quadrant I.

True

False

3) Which pair of ordered pairs identifies points F and J correctly?

a.) F(1, 0), J(2, 0)

b.) F(0, 1), J(0, 2)

c.) F(0, 1), J(2,0)

d.) F(1,0), J(0, 2)

4) Which statement does NOT describe the given points?

a.) The x-coordinate of point B is positive and the y-coordinate is negative.

b.) Both the x- and y-coordinates of points G and D are positive.

c.) The x- and y-coordinates of point H are negative.

d.) The x-coordinates of points C and E are positive and the y-coordinates are negative.

e.) The y-coordinate of point J is zero.

5) Consider an isosceles triangle with the following vertices: (0, 4), (2, –3), and (x, y). Which set of coordinates can be used to complete the isosceles triangle?

a.) (–2, –3)

b.) (–3, –3)

c.) (–2, –2)

d.) (–2, 3)

6) Consider a rectangle with the following coordinates: (4, 1), (4, –4), (–2, –4), and (x, y). Which set of coordinates can be used to complete the rectangle?

a.) (2, –1)

b.) (2, 4)

c.) (–2, 1)

d.) (–2, –1)

7) Consider the parallelogram with the following coordinates: (–4, –1), (–2, 3), (3, 2) and (x, y). Which set of coordinates can be used to complete the parallelogram?

a.) (0, –2)

b.) (1, –2)

c.) (2, –1)

d.) (1, –1)

8) If point T is placed in Quadrant III to form parallelogram RSQT, what are point T’s coordinates?

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9) If point T is placed in Quadrant I to form trapezoid STQR such that the non-parallel sides are congruent, what are point T’s coordinates?

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10) Which statement describes the translation that occurs from parallelogram ABCD to parallelogram A'B'C'D'.

a.) Parallelogram ABCD is translated five (5) units to the left and four (4) units down.

b.) Parallelogram ABCD is translated five (5) units to the right and four (4) units down.

c.) Parallelogram ABCD is translated four (4) units to the left and five (5) units down.

d.) Parallelogram ABCD is translated four (4) units to the right and five (5) units down.

11) Describe the translation that occurs from trapezoid ABCD to trapezoid A'B'C'D'.

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12) Triangle DEF has vertices D(–3, –4), E(–3, –1), and F (–1, –4). Print out the graph below and perform the translation. Name the image, triangle D'E'F'. Which set of coordinates denote triangle D'E'F'?

a.) D'(2, –1), E'(2, 2), F'(4, –1)

b.) D'(2, –1), E'(2, 1), F'(4, 0)

c.) D'(2, –2), E'(2, 0), F'(4, –1)

d.) D'(2, 0), E'(2, 2), F'(4, 1)

13) The vertices of polygon JKLMN are J(–3, 2), K(–2, 1), L(1, 1), M(1, –2), and N(0, –4). Print out the coordinate plane shown below and complete the following activity. First, graph polygon JKLMN and second, graph its image indicated by the given translation. Name the image, J'K'L'M'N'. Which set of coordinates denote polygon J'K'L'M'N'?

a.) J'(–4, 0), K'(–3, –1), L'(0, –1), M'(0, –4), N'(–1, –6)

b.) J'(–1, 3), K'(0, 2), L'(3, 2), M'(3, –1), N'(2, –3)

c.) J'(–5, 3), K'(–4, 2), L'(–1, 2), M'(–1, –1), N'(–2, –3)

d.) J'(–5, 1), K'(–4, 0), L'(–1, 0), M'(–1, –3), N'(–2, –5)

14) Print out the coordinate plane below and complete the following activity. Draw and label triangle DEF with vertices D(–2, 1), E(1, 5) and F(2, 3). Translate triangle DEF according to the description of Translation 1 and name the triangle D’E’F’. Translate triangle D’E’F’ according to the description of Translation 2 and name the triangle D’’E’’F’’. State the letter and ordered pair for the vertices of the image (triangle D''E''F'').

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15) In the previous problem, if triangle DEF was directly translated to triangle D''E''F'', describe the movements necessary to perform the single translation of each vertex from triangle DEF to triangle D''E''F''.

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16) Use coordinate notation to denote the translation from figure A to figure B.

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17) Use coordinate notation to denote the translation from figure C to figure D.

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18) How many lines of symmetry does an equilateral triangle have?

a.) 1

b.) 2

c.) 3

d.) 4

19) Which segment is a line of symmetry for the square and the decagon shown below?

a.) Segment AC

b.) Segment BD

c.) Segment DH

d.) Segment AE

20) Which line is the line of symmetry of the reflection shown below?

a.) x-axis

b.) y-axis

c.) origin

d.) a diagonal line passing through point (0, 2)

21) Describe how the image in Quadrant II could be changed so that it would be a reflection of the image in Quadrant I?

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22) The vertices of quadrilateral ABCD are given below. Print out the coordinate plane and complete the given reflection. What are the coordinates of the image? Include the name of each vertex.

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23) Trapezoid DEFG has vertices D(–4, 1), E(–5, 4), F(–1, 4), and G(–2, 1). Print out the graph below and perform the translations. What are the coordinates of image D''E''F''G''? Include the name of each vertex. Be careful with this problem and make sure that the vertices are named correctly after each transformation.

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24) Figure AB has been rotated 90-degrees clockwise around the origin of the coordinate plane. Write the ordered pairs for points A’ and B’. Which phrase completes the following statement? When rotating a figure in the coordinate plane about the origin and using a 90-degree clockwise rotation, the vertices of the rotated figure will change as follows:

a.) the x-coordinate will become the y-coordinate and the y-coordinate will become the x-coordinate.

b.) the x-coordinate will become the opposite of the y-coordinate and the y-coordinate will become the x-coordinate.

c.) the x-coordinate will become the opposite of the y-coordinate and the y-coordinate will become the opposite of the x-coordinate.

d.) the x-coordinate will become the y-coordinate and the y-coordinate will become the opposite of the x-coordinate.

25) Complete the figure by drawing and rotating copies of the kite counterclockwise around the origin of the coordinate plane so that the shorter edges of the kites touch, but do not overlap. Describe the completed figure and how many kites make up the completed figure.

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26) Jerry's CD player can hold five compact disks on a rotating tray around point A. The CD tray can move only counterclockwise. Answer the following questions: (a) How many degrees does the tray rotate from one position to the next? (b) How many degrees will the tray rotate to play a CD in position 4 if the starting position is position 1? (Hint: If CD 1 moves counterclockwise from its original position completely around and back to its original position, it will have rotated 360 degrees around center point A.)

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27) Select the terms that complete the following statements correctly: If the scale factor for a dilation is less than one, the image is _______. If the scale factor for a dilation is greater than one, the image is _____.

a.) enlarged, enlarged

b.) reduced, enlarged

c.) enlarged, reduced

d.) reduced, reduced

28) True or False. The image below shows an example of a dilation.

True

False

29) The vertices of the triangle are A(–2, 1), B(–1, 3), and C(2, –1). After a dilation having a scale factor of three (3) is performed where the scale factor is applied to both the x- and y-coordinates, what are the vertices of the image, A'B'C'?

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30) Compare the lengths and widths of the image (smaller picture) and its dilation. What is the scale factor of the dilation based on the length and width of the picture?

a.) 2.5

b.) 3

c.) 3.5

d.) 4

31) In the figure trapezoid A'B'C'D' is the image of trapezoid ABCD after a dilation is performed. What is the scale factor?

a.) 1/4

b.) 1/2

c.) 2

d.) 3

32) Quadrilaterals can be used to create attractive tessellations. A quadrilateral is shown below and transformed to demonstrate how it can be used to tessellate a plane. Draw a quadrilateral of your choice and transform (translate, rotate, and/or reflect) it several times to tessellate a plane. If you have access to a scanner, attach a scanned picture of your tessellation. If not, describe your tessellation and the transformations that you used to tessellate the plane.

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33) M.C. Escher was an artist who blended the mathematics of tessellations and his artistic talent to create compelling drawings that tessellated a plane. Go to the official Escher website, http://www.mcescher.com/, and navigate the site to find the gallery of his drawings that display symmetry. Choose your favorite Escher print and describe how he used tessellations to create the drawing. Make sure you spend ample time studying the picture as you may find shapes that at first glance you did not notice. You may attach the picture you chose to share with the instructor.

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