1. PRE-ALGEBRA 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’. 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’. -5 3

2. PRE-ALGEBRA “Rotations” (9-10) A rotation is a turn about a fixed point called the “center of rotation”. What is a “rotation”? Example: In the diagram below,  QPR is rotated about the point P, so P is the center of rotation. What is the “angle of rotation”. The angle of rotation is the measurement of the rotation or turn in degrees. Example: In the diagram above,  QPR is rotated 90 0. Notice that when the triangle is turned 90 0, the resulting angles QPQ’ and RPR’ also equal 90 0. What is “rotational symmetry”. A figure has rotational symmetry when you can turn it 180 0 or less and it looks exactly the same as it did before the rotation. Example: Each time you turn the wheel below 72 0 (360 0  5 = 72 0 ), it will look exactly like it did before the turn. Each time you turn the below 120 0 (360 0  3 = 120 0 ), it will look exactly like it did before the turn.

3. PRE-ALGEBRA 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. Rotations LESSON 9-10 Additional Examples Find the vertices of the image of RST after a rotation of 90° counterclockwise about the origin. Step 2 Turn your paper counterclockwise (opposite direction the hands on a clock move) to see what the rotated image looks like.

4. PRE-ALGEBRA (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). Rotations LESSON 9-10 Additional Examples

5. PRE-ALGEBRA Judging from appearance, tell whether the star has rotational symmetry. If so, what is the angle of rotation? 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°. Rotations LESSON 9-10 Additional Examples Rotate the paper to see how many positions look exactly like the original star.