Rotations – Discovery Activity



Rotations around the Origin – Discovery Activity Name_______________________________

Date_____________________Pd_________

In this activity, you will use the pegboard, pegs, and rubber bands provided to help you explore what happens to a segment when you rotate it 90°, 180°, and 270° around the origin. As you progress through the activity, you will discover the rules for rotating any point, segment, or other figure around the origin. ROTATIONS ARE ALWAYS COUNTER CLOCKWISE (unless the directions state clockwise)

1. Make sure your pegboard has the x and y axis attached.

2. Take one red peg, one blue peg, and one rubber band and use them to make a segment entirely contained in the first quadrant. Your segment should not be horizontal or vertical.

3. Fill in the table using your pegboard to help you. Actually rotate your pegboard by each degree measure and record the coordinates of the new points after the rotations. Be sure to rotate counterclockwise.

|Original segment |Segment after 90° rotation |What is the rule in general for a 90° |

|Red point ( ____, ____ ) |Red point ( ____, ____ ) |rotation around the origin? |

| | |(In terms of x and y) |

|Slope: ______ Blue point ( ____, ____ ) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ |What is the equation? |

| | | |

|Original segment |Segment after 180° rotation |What is the rule in general for a 180° |

|Red point ( ____, ____ ) |Red point ( ____, ____ ) |rotation around the origin? (In terms of x|

| | |and y) |

|Slope: ______ Blue point ( ____, ____ ) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ |What is the equation? |

| | | |

|Original segment |Segment after 270° rotation |What is the rule in general for a 270° |

|Red point ( ____, ____ ) |Red point ( ____, ____ ) |rotation around the origin? (In terms of x|

| | |and y) |

|Slope: ______ Blue point ( ____, ____ ) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ |What is the equation? |

| | | |

4. Exchange papers with a partner and verify that you have come up with the same rule.

5. Using your rules from above, predict (without actually rotating your board yet) what will happen to the segments after rotations of 90°, 180°, and 270° and write the equation. Write those predictions in this table:

|Original segment |Segment after 90° rotation |What is the rule in general for a 90° |

|Red point ( 0 , 0 ) |Red point ( ____, ____ ) |rotation around the origin? |

| | |(In terms of x and y) |

|Slope: ______ Blue point ( 3, 1 ) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ | |

|Original segment |Segment after 180° rotation |What is the rule in general for a 180° |

|Red point ( 2 , -2 ) |Red point ( ____, ____ ) |rotation around the origin? (In terms of x|

| | |and y) |

|Slope: ______ Blue point ( 4 , -4 ) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ | |

|Original segment |Segment after 270° rotation |What is the rule in general for a 270° |

|Red point ( -1, -2 ) |Red point ( ____, ____ ) |rotation around the origin? (In terms of x|

| | |and y) |

|Slope: ______ Blue point ( -3 , -4) |Slope: ______ Blue point ( ____, ____ ) | |

| | |(x, y) ( ( _____, _____ ) |

|Equation of line: ______________________ |Equation of line: ______________________ | |

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