Transcript Rotations

Warm-Up for Lesson 9-10
When you write a rule to describe a translation, you can choose corresponding
(matching) points on a figure and it’s image (for example, A and A’ or B and B”). You
simply subtract the coordinates of the figure from the coordinates of it’s image to find the
translation.
Write the rule to describe the translation of
PQR to P’Q’R’.
-5
3
Use one of the points, like P (3,2), and
it’s image, P’ (-2,5) to find the horizontal
and vertical translations.
Horizontal translation: (-2) – (3) = -5
Vertical translation: (5) – (2) = 3
The rule is  (x - 5, y + 3)
Write the rule to describe the translation of
quadrilateral ABCD to A’B’C’D’.
PRE-ALGEBRA
“Rotations”
(9-10)
What is a
“rotation”?
A rotation is a turn about a fixed point called the “center of rotation”.
Example: In the diagram below, QPR is rotated about the point P, so P is the center
of rotation.
What is the The angle of rotation is the measurement of the rotation or turn in degrees.
Example: In the diagram above, QPR is rotated 900. Notice that when the triangle is
“angle of
turned 900, the resulting angles QPQ’ and RPR’ also equal 900.
rotation”.
What is
“rotational
symmetry”.
A figure has rotational symmetry when you can turn it 1800 or less and it looks
exactly the same as it did before the rotation.
Example: Each time you turn the wheel below 720 (3600 5 = 720), it will look exactly
like it did before the turn. Each time you turn the below 1200 (3600 3 = 1200), it will
look exactly like it did before the turn.
PRE-ALGEBRA
Rotations
LESSON 9-10
Additional Examples
Find the vertices of the image of
90° counterclockwise about the origin.
RST after a rotation of
Step 1 Use a blank transparency sheet.
Trace RST, the x-axis, and the y-axis.
Then fix the tracing in place at the origin.
Step 2 Turn your paper counterclockwise
(opposite direction the hands on a clock
move) to see what the rotated image looks
like.
PRE-ALGEBRA
Rotations
LESSON 9-10
Additional Examples
(continued)
Step 3 Label the vertices of the rotated image
R’ , S’ , and T’ . Then, connect the vertices
of the rotated triangle..
The vertices of the image are
R’ (1, 1), S’ (4, 1), and T’ (4, 5).
PRE-ALGEBRA
Rotations
LESSON 9-10
Additional Examples
Judging from appearance, tell whether the star has
rotational symmetry. If so, what is the angle of rotation?
Rotate the paper to see how many positions look exactly like the original star.
The star can match itself in 6 positions.
The pattern repeats in 6 equal intervals. 360° ÷ 6 = 60°
The figure has rotational symmetry.
The angle of rotation is 60°.
PRE-ALGEBRA