Unit 9: Transformations Review

Unit 9: Transformations Review

THINK ABOUT IT!

What does it mean for a figure to be congruent? Similar?

Which transformations result in congruent figures?

What transformation results in a similar figure?

Multiple Choice

#1. A rotation of 360 degrees counterclockwise will...

• move the image two quadrants to the right?

• map an image onto itself

• always be found in quadrant II

• move the image 5 units left and 2 units up

Multiple Choice

#2. Which of the following transformations has the same result as a rotation of 270 degrees counterclockwise?

• Translation 7 units to the right

• Reflection over the x-axis

• Dilation of a scale factor of 5

• Rotation of 90 degrees clockwise

Multiple Choice

#3. The translation (x - 4, y + 14) is applied to a rectangle. Jean makes a conjecture about the perimeter of the image of the rectangle, tests the conjecture, and finds that it is true. What could have been his conjecture?

• The perimeter of the image is 14 times the perimeter of the original rectangle.

• The perimeter of the image is 4 units shorter than the perimeter of the original rectangle.

• The perimeter of the image is the same as the perimeter of the original rectangle.

• The perimeter of the image is 18 times larger than the original image.

Multiple Choice

#4. A dilation will result in an image which is

• Similar and congruent to the pre-image.

• Similar but NOT congruent to the pre-image.

• An image that is rotated.

• An image that is a reflection of the pre-image.

TRANSLATIONS

SLIDES all points of the figure right/left/up/down the same number of units.

Pre-Image & Image are congruent.

See image for algebraic representation.

Multiple Choice

#12. Shawn graphs a square. The square is translated 5 units left and 3 units down. How do the angles in the image square compare to the angles in the original square?

• The angles are five times greater.

• The measure of the angles decrease by 3.

• The measures of the angles are the same.

• Angle A and B decrease, while angle C and D increase.

Multiple Choice

#7. If rectangle ABCD is translated 2 units down and 7 units to the left, which best represents the coordinates of the new figure?

• A’ (6,4) B’ (3,4) C’(6,6) D’(3,6)

• A’ (-4, 6) B’ (4, -3) C’ (6, -6) D’ (-3, 6)

• A’ (-6, -6) B’(-3, -6) C’ (-3, -4) D’(-6, -4)

• A’ (-6, 6) B’(-3, 6) C’ (3, -4) D’(-6, 4)

Reflections

FLIPS a figure over the x- or y-axis.

Pre-Image & Image are congruent.

See image for algebraic representation.

Multiple Choice

#13 Polygon LMKN is shown on the coordinate grid. A student reflected the polygon across the y-axis to create a polygon L’M’K’N’.

Which rule describes this transformation?

• (x, y) - > (x+4, y)

• (x, y) - > (-y, x)

• (x, y) - > (-x, y)

• (x, y) - > (x, -y)

Multiple Choice

#9 Triangle KLM is shown on the graph below. If triangle KLM is reflected over the y-axis, what is the coordinate of L’?

• (-2, 1)

• (7, 4)

• (-7, -4)

• (-7, 4)

Rotations

TURNS a figure about the origin.

Pre-Image & Image are congruent.

See image for algebraic representation. (PAY ATTENTION TO WHICH RULES ARE THE SAME!)

Multiple Choice

#6. Mary draws two figures on a coordinate plane. What type of transformation is shown?

• Reflection

• Translation

• Rotation

• Dilation

Multiple Choice

#14. Jerry graphed a triangle on the coordinate grid shown.

Jerry rotated the triangle 270°counterclockwise about the origin to create figure A’B’C’. What are the coordinates of the vertices of the figure A’B’C’ after the

• A’(-3 ,2 ), B’(-4, 5), C’(-4, 2)

• A’(3 ,-2 ), B’(4, -5), C’(-4, -2)

• A’(-2 ,-3 ), B’(-5, -4), C’(-2, -4)

• A’(-3 ,-2 ), B’(-4, -5), C’(-4, -2)

Dilations

ENLARGES (grows) or SHRINKS (makes smaller) figures.
Pre-Image & Image are SIMILAR.
See image for algebraic representation.

SCALE FACTOR:

 $\frac{image}{pre-image}$  

Multiple Choice

 #8. Triangle ABC is dilated with the origin as the center of dilation to create triangle A’B’C’.
Which rule best represents the dilation that has been applied to triangle ABC to create triangle A’B’C’?

•   $(x,y)->(x+4,y-2)$    

•   $(x,y)->(x-3,y+2)$  

•  $(x,y)->(12x,12y)$  

•  $(x,y)->(2x,2y)$  

Multiple Choice

#18. Lilly enlarged a plan for an outdoor stage. The original plan is to the left. She dilated the stage by a scale factor of six with the center of dilation at the origin. Which ordered pair will be the coordinates of one of the new vertices?

• (24,5)

• (18, 30)

• (1, 2)

• (24, 30)

Identify Sequences of Transformations

Pay attention to Quadrants and what coordinates are like in each.

Pay attention to whether the figure flips over or is upside down.

Multiple Choice

#5. Are trapezoids ABCD and A’B’C’D’ congruent? If so, what is the sequence of transformations that maps ABCD to A’B’C’D’?

• No, there is no sequence of transformations that maps ABCD to A’B’C’D’

• Yes, reflect across the x-axis and then translate it 6 units right

• Yes; reflect across the y-axis and then rotate 270 clockwise about the origin.

• Yes; rotate 90 clockwise and then translate 6 units right.

Multiple Select

#10 A quadrilateral EFGH is translated 4 units up and 2 units to the right and then rotated 180 degrees about the origin to form quadrilateral E’F’G’H’.

Select the two true statements.

• The length of line segment E’H’ is 10 units.

• The length of line segment F’G’ is 8 units.

• The length of line segment F’E’ is 5 units.

• The length of line segment E’H’ is 6 units.

• The length of line segment F’G’ is 11 units.

Complete study guide questions: 11,15, 16, 17, 19 and 20. Remember, the test will look similar to this study guide.

• Watch the study guide video to hear a review again of what you need to do for each question tomorrow.

• Complete any missing IXL work or Edpuzzle work.