Look at the figure on the left and its image on the right.

Which of these describes the transformation of the original figure onto its image?

What is the appearance of the picture in the mirror?

ΔPQR has been translated to the position of ΔP'Q'R'. Rectangle WXYZ will be translated to a corresponding position using the same transformation.

What is the location of X' in the new rectangle?

A line segment on the coordinate plane joins (0, 5) to the origin. After a rotation the slope of this segment is 0. Which of these could be the angle of rotation?

A triangle with vertices at (0, 0), (0, 6), and (4, 0) is shown on the grid below.

• Draw the dilation image of the triangle using a scale factor of 3 and using (0, 0) as the center of the dilation on the grid provided in the Answer Book.
   
• What is the difference between a dilation using a scale factor greater than 1 and a dilation using a scale factor between 0 and 1? Use examples to justify your answer.
   

• Draw the reflection of the figure over line .
   
• Explain the steps you used to draw the reflection of the figure.
   
• Explain the relationship of the distance between line and point D to the distance between line and point D'.
   

A fan has 5 congruent blades that are spaced equally as shown below.

What is the measure of the angle of rotation if blade M moves clockwise to the position of blade P ?

Which of these transformations can change the area of a polygon?

A person playing miniature golf hits the ball from point T to point M on the wall. The path of the ball after it bounces off the wall will be the reflection of line TM across the dotted line.

Which point will the ball pass through?

A member of the Boating Club created a design with two boats. The two boats in the design are related only by a translation. Which of these could be the design?

Figure ABCD is shown on the grid below.

Use the answer box to complete the following. (You will also need to use graph paper to complete the answer satisfactorily.)

• On a grid, reflect ABCD across the y-axis. Label the image A'B'C'D'.
   
• Use mathematics to explain how a reflection across the y-axis affects the coordinates of any point (x, y). Use words, symbols, or both in your explanation.
   
• On the same grid, translate A'B'C'D' 6 units down. Label the image of this translation A"B"C"D".
   
• Use mathematics to explain how a translation 6 units down affects the coordinates of any point (x, y). Use words, symbols, or both in your explanation.

Many clocks and calculators use digital numbers like the ones shown below. Of the first three numbers, only 1 and 3 will appear the same when reflected about line .

Which of these remaining numbers will also look the same when reflected over line ?

A rectangular lot is plotted on a coordinate plane. A flagpole will be moved from its location at the coordinates (1,2) to the left 3 units. What are the new coordinates of the flagpole?

• Sketch the positions of the three new houses and their garages. Use mathematics to describe the transformation or transformations needed to reproduce the houses and garages from lot A to lot B, lot B to lot C, and lot C to lot D.

A dilation with center P maps the rectangle RSTU to the rectangle as shown below.

What is the scale factor of this dilation?

A translation maps L to L' as shown below. Using the same translation, P is mapped to P'.

What are the coordinates of P'?

Look at the figure below.

Which of these shows a 270° clockwise rotation of the figure?

The figure below is to be reflected first over the x-axis and then over the y-axis.

Which of these diagrams represents the resulting figure?

Triangle PQR is shown below.

What is the image of point Q after a rotation of 90° counterclockwise about the origin?

Triangle PQR is shown below. Triangle PQR will be mapped to its image P'Q'R'. This will be done by increasing each of its x-coordinates by 5.

Which term best describes the transformation?

Look at figure ABCDE below.

• Draw the reflection of figure ABCDE over line m. Label the corresponding vertices A'B'C'D'E'.
   
• What is the relationship between ABC and A'B'C'? Use mathematics to justify your answer.
   

Which of these transformations in the coordinate plane can change the area of a geometric figure?