Unit 2 Worksheet



Unit 5 From the EOCT Study Guide p. 165 Name________________________________

|Name each geometric figure (using traditional shorthand notation) and make sure |Transformations we need to know: translation, rotation, reflection, and dilation.|

|you fully understand each definition. | |

| |Translations: |

|Definition |“Translate” => “Move” |

|Sketch |[pic] |

|Name | |

| |Ex) [pic]ABC has been translated left 2 and up 3units. |

|1.) A line segment is part of a line; it consists of two endpoints and all points| |

|between them. |[pic] |

| | |

|[pic] |[pic]ABC is the pre-image (where we started) |

| |[pic] A'B'C' is the image (where we ended up) |

| | |

|2.) An angle is formed by two rays with a common endpoint. |6.) Compare the distance from A to A' to the distance from B to B' to the |

| |distance from C to C' |

|[pic] | |

| | |

| |7.) What is true about the lines [pic], [pic], and [pic]? |

|3.) A circle is the set of all points in a plane that are a fixed distant from a | |

|given point, called the center; the fixed distance is the radius. |8.) Where was C mapped to? |

| |(x, y) ( (x – 2, y + 3) |

|[pic] |Inputs Outputs |

| |A(1,1) [pic]A'(-1, 4) |

| |B(6,5) [pic]B'(4, 8) |

| |C(7,1) [pic]C'(__________) ( fill in the blank |

|4.) Parallel lines are lines in the same plane that do not intersect. | |

| | |

| |Ex2) [pic]ABC has been reflected over the x-axis |

|[pic] | |

| |[pic] |

| | |

| |13.) What are the coordinates of the vertices in the pre-image? |

|5.) Perpendicular lines are two lines that intersect to form right angles. | |

| |14.) What are the coordinates of the vertices in the image? |

| | |

| |15.) Which formula describes a reflection over the |

|[pic] |x-axis? |

| |a.) (x, y) ( (y, x) |

| |b.) (x, y) ( (-x , -y) |

| |c.) (x, y) ( (-x , y) |

| |d.) (x, y) ( (x , -y) |

|Reflections: | |

| |Ex3) [pic]ABC has been reflected over y = x |

|[pic] |[pic] |

| | |

| |16.) What are the coordinates of the vertices in the pre-image? |

|Ex) [pic]ABC has been reflected over the y-axis | |

| |17.) What are the coordinates of the vertices in the image? |

|[pic] | |

| |18.) Which formula describes a reflection over the line y = x? |

|9.) What line is the perpendicular bisector of [pic] ? |a.) (x, y) ( (y, x) |

| |b.) (x, y) ( (-x , -y) |

|10.) What are the coordinates of the vertices in the pre-image? |c.) (x, y) ( (-x , y) |

| |d.) (x, y) ( (x , -y) |

|11.) What are the coordinates of the vertices in the image? | |

| |24.) Alex says the formula to rotate 180( about the origin is (x, y) ( (-x ,|

|12.) Which formula describes a reflection over the |-y) |

|y-axis? |Let A(3, 2), B(7, 4), and C(4, 8) be the vertices of [pic]ABC. Find the vertices|

|a.) (x, y) ( (x – 2, y + 3) |of the image after using Alex’s formula. What can you conclude? |

|b.) (x, y) ( (-x , -y) | |

|c.) (x, y) ( (-x , y) |[pic] |

|d.) (x, y) ( (x , -y) | |

| | |

| |25.) Which of these can you name? |

| | |

| |a.) (x, y) ( (x, -y) _________________________ |

|Rotations: | |

| |b.) (x, y) ( (-x, y) ________________________ |

|[pic] | |

| |c.) (x, y) ( (-x, -y) ________________________ |

| | |

| |d.) (x, y) ( (y, x) _________________________ |

|Ex1) [pic]ABC has been rotated 90( CW about (0, 0) | |

|[pic] |e.) (x, y) ( (-y, x) _________________________ |

| | |

|19.) What are the coordinates of the vertices in the pre-image? |f.) (x, y) ( (y, -x) _________________________ |

| | |

|20.) What are the coordinates of the vertices in the image? |g.) (x, y) ( (-y, -x) ________________________ |

| | |

|21.) Which formula describes a rotation of 90( CW about the origin or point (0, |h.) (x, y) ( (x + 1, y – 2) ___________________ |

|0)? | |

|a.) (x, y) ( (y, x) |26.) A(1, 2), B(2, 3), C(3, 2), D(2, 1) |

|b.) (x, y) ( (-x , y) |Where would the figure ABCD be after undergoing the following transformations? |

|c.) (x, y) ( (-y , x) |(x, y) ( (x, y + 5) |

|d.) (x, y) ( (y , -x) | |

| | |

|22.) Rotating a figure 90( CW about the origin is the same as rotating a figure: | |

|a.) 90( CCW about the origin |27.) BIG IMPORTANT QUESTION! Has the size of any triangle changed with any of |

|b.) 180( CCW about the origin |these transformations? |

|c.) 360( CCW about the origin | |

|d.) 270( CCW about the origin |If the size of the figure doesn’t change after undergoing the transformation, the |

| |transformation is known as rigid |

|23a.) Rotating something 90( CCW would be the same as… | |

|b.) Rotating something 180( CCW would be the same as… |In geometry, we say shapes are congruent when they are the same size. The symbol|

| |for congruent is (. |

|Dilations: | |

|28.) Plot the points A(-2, -3), B(1, -2), C(-2, 1). If I wanted this triangle | |

|increase in size, I could dilate each input by a factor of 2 using (x, y) ( (2x, | |

|2y). What would the new coordinates be? Plot them on the same coordinate plane |36a.) Which transformation is shown here? |

|as the pre-image. |[pic] |

| | |

|[pic] |b.) Was this a rigid transformation? |

| | |

|29.) Is a dilation a rigid transformation? Explain. |c.) Did the angle measures change? |

| | |

| |37a.) Which transformation is shown here? |

|In geometry, we say shapes are similar when they are the same shape (same angle |[pic] |

|measures) but different sizes. The symbol for similar is ~. | |

| |b.) Was this a rigid transformation? |

| | |

|30.) If [pic]ABC is translated to[pic]A'B'C', which is true? |c.) Did the angle measures change? |

|a.) [pic]ABC ( [pic]A'B'C' b.) [pic]ABC ~ [pic]A'B'C' | |

| |38.) What transformations could have gotten us from figure 1 to figure 2? |

|31.) If [pic]ABC is rotated to[pic]A'B'C', which is true? |[pic] |

|a.) [pic]ABC ( [pic]A'B'C' b.) [pic]ABC ~ [pic]A'B'C' | |

| |39.) If we know that ABCD → EFGH, which transformation is shown? (one answer) |

|32.) If [pic]ABC is dilated to[pic]A'B'C', which is true? |[pic] |

|a.) [pic]ABC ( [pic]A'B'C' b.) [pic]ABC ~ [pic]A'B'C' | |

| |42.) A(1, 2), B(2, 3), C(3, 2), D(2, 1) |

|33.) If [pic]ABC is reflected to[pic]A'B'C', which is true? |Where would the figure ABCD be after undergoing the following 6 transformations? |

|a.) [pic]ABC ( [pic]A'B'C' b.) [pic]ABC ~ [pic]A'B'C' |1st: (x, y) ( (x, y + 5) 5th: (x, y) ( (3x, y) |

| |2nd: (x, y) ( (x, y – 5) 6th: (x, y) ( ([pic]x, y) |

| |3rd: (x, y) ( (x + 3, y) |

|34.) Which moves an object 2 units down? |4th: (x, y) ( (x – 3, y) |

|A. (x, y) ( (x + 2, y) C. (x, y) ( (x, y + 2) | |

|B. (x, y) ( (x – 2, y) D. (x, y) ( (x, y – 2) |43.) Which (one) transformation would map this figure back onto itself? |

| |[pic] |

|35.) Reflect the quadrilateral over the x-axis. Draw it. | |

|[pic] | |

| |44.) Name 3 different (single) transformations that would map this figure to |

|40.) What sequence of events could get us from ABCD to PQRS???? |itself. |

|[pic] |[pic] |

| | |

|A Possible Solution to #40 |Rotational Symmetry: |

|[pic] |45.) Describe every rotation that maps this figure to itself: a regular hexagon |

| |centered about the origin, which has a vertex at (4, 0). |

|41.) What sequence of events could get us from ABCD to PQRS???? |[pic] |

|[pic] | |

| | |

|A Possible Solution to #41 |2) A parallelogram has vertices at (0, 0), (0, 6), (4, 4), and (4, –2). |

|[pic] |[pic] |

| |Which transformation maps the parallelogram to itself? |

|Note that A' and P are the same point. |A. a reflection across the line x = 2 |

| |B. a reflection across the line y = 2 |

| |C. a rotation of 180° about the point (2, 2) |

| |D. a rotation of 180° about the point (0, 0) |

| | |

| |3) Which sequence of transformations maps [pic]ABC to[pic]RST ? |

| |[pic] |

|46.) Describe every reflection that maps this figure to itself: a regular hexagon| |

|centered about the origin, which has a vertex at (4, 0). |A. Reflect [pic]ABC across the line x = –1. Then translate the result 1 unit down.|

|[pic] | |

| |B. Reflect [pic]ABC across the line x = –1. Then translate the result 5 units |

| |down. |

| | |

| |C. Translate [pic]ABC 6 units to the right. Then rotate the result 90° clockwise |

| |about the point (1, 1). |

| | |

| |D. Translate [pic]ABC 6 units to the right. Then rotate the result 90° |

| |counterclockwise about the point (1, 1). |

| | |

| | |

| | |

| | |

| | |

|EOCT Practice: | |

|1) A regular pentagon is centered about the origin and has a vertex at (0, 4). | |

|[pic] | |

| | |

|Which transformation maps the pentagon to itself? | |

|A. a reflection across line m | |

|B. a reflection across the x-axis | |

|C. a clockwise rotation of 100° about the origin | |

|D. a clockwise rotation of 144° about the origin | |

| | |

| | |

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A rotation of x( about a point Q maps every point S to S' so that the following properties are true:

• SQ = S'Q and

m(SQS' = x(

• Preimage point Q and image point Q' are the same.

Note that [pic] and [pic] are radii of (Q

…

Translate ABCD down 5 units to get A'B'C'D'. Then rotate A'B'C'D' clockwise 90( about point B' to obtain PQRS.

Reflect ABCD across the line x = 2 to obtain A'B'C'D'. Then rotate A'B'C'D' 180( about the point A' to obtain PQRS.

A translation maps points P and Q to point P' and Q' so that the following properties are true:

• PP' = QQ'

• [pic] (( jarT[pic]h¤^U[pic]V[pic]j>h¤^U[pic]j

rT[pic]h¤^U[pic]V[pic]j‘h¤^U[pic]jãqT[pic]h¤^U[pic]V[pic]jh¤^U[pic]hà2ú EMBED Equation.3 [pic]

A. (x, y) → (2x, y)

B. (x, y) → (x, 2y)

C. (x, y) → (x+2, y)

D. (x, y) → (x, y+2)

A. (x, y) → (2x, y)

B. (x, y) → (x, 2y)

C. (x, y) → (x+2, y)

D. (x, y) → (x, y+2)

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