6th Grade Math Textbook, Fundamentals

&KDSWHU 

0RUH(QULFKPHQW7RSLFV

Use grid paper to make a coordinate plane for each problem.

1.Draw a quadrilateral in Quadrant I with a vertex at (1, 1).

Starting with your quadrilateral, perform the following

translations in order: reflect over the x-axis, translate left

10 units, reflect over the x-axis, and translate right 10

units. How does the position of the final image relate to

the position of the pre-image?

2.Draw a scalene triangle in Quadrant III. If it is rotated

360° about the origin, it will return to its original position.

Find a combination of two or more transformations that

will also return the triangle to its original position.

3.Draw a pre-image square in Quadrant II. Rotate it 180°

about the origin to obtain an image. Find a combination

of two transformations that will give the same image.

4.Discuss and Write Choose a figure and a transformation. Then tell how

to find a combination of transformations that result in the same image.

pages 425–426 for exercise sets.

What happens when isosceles trapezoid TRAPis
first reflected over the x-axis and then rotated 270°
counterclockwise about the origin?

Draw a trapezoid on a grid and perform these two
transformations.

You can see that TRAPis congruent to trapezoid
TRAPand to trapezoid TRAP. The only
change has been in the position of trapezoid TRAP.

There are other ways that isosceles trapezoid

TRAPcan be transformed into the image

TRAPlike the following:

• Rotate TRAPcounterclockwise 90° about the
  origin and then reflect over the x-axis.


• Reflect TRAPover the y-axis and then rotate
  it 90° counterclockwise about the origin.
  (You might try these transformation combinations,
  starting with a trapezoid that is not isosceles.)
  You can perform as many transformations as you
  like on a figure.
  Suppose that you now want TRAPto move to a
  position in Quadrant II. To do this you can choose
  from translating it up at least 5 units, rotating it 270°
  counterclockwise about the origin, or reflecting it
  over the x-axis.

T‘ R‘

T R

A‘

AP

A“

P“

R“

y

x

4XDGUDQWII 4XDGUDQWI

4XDGUDQWIII 4XDGUDQWIV

P‘

T“