6th Grade Math Textbook, Fundamentals

Graph line segmentDE with endpoints D(1, 1) and

E(3, 3). Rotate the line segment 90 counterclockwise.

Then write the coordinates of the image.

Use the rule for rotating a figure 90 counterclockwise.

x y

yx

D(1, 1) D(1, 1)

E(3, 3) E(3, 3)

The coordinates of line segmentDEare D(1, 1) and E(3, 3).

1

Lesson 13-11 for exercise sets. &KDSWHU 

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1.Draw MNOwith vertices M(0, 0), N(1, 4), O(2, 2). Rotate the triangle 180

around the origin. What are the coordinates of the vertices of the image?

2.Draw rectangle RSTUwith vertices R(1, 1), S(5, 1), T(5, 6), U(1, 6). Rotate

the rectangle 90 counterclockwise around the origin. What are the coordinates

of the vertices of the image?

3.Discuss and Write Suppose you rotate line segment DE(see the graph above)

180° counterclockwise around the origin. How would this transformation compare

to reflecting line segment DEover the line that includes line segment DE?

Explain your answer.

You can write rules to describe the coordinates of an image under 90 ,

180

 , and 270 rotations around the origin.

For each rotation on page 372, examine the coordinates of the original

figure with the coordinates of its image. What do you notice?

• To rotate a figure 270 counterclockwise around the origin, switch the
  coordinates of each point and then multiply the new second coordinate by 1.

270 Counterclockwise Rotation:

A(3, 0), B(5, 2), C(0, 1) A(0, 3), B(2, 5), C(1, 0)

• To rotate a figure 90 counterclockwise around the origin, switch the
  coordinates of each point and then multiply the new first coordinate by 1.

90 Counterclockwise Rotation:

A(3, 0), B(5, 2), C(0, 1) A(0, 3), B(2, 5), C(1, 0)

• To rotate a figure 180 around the origin, multiply both coordinates by 1.

180 Counterclockwise Rotation:

A(3, 0), B(5, 2), C(0, 1) A(3, 0), B(5, 2), C(0, 1)

y

x

  



















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D

E

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