Sewanhaka High School
Math 8A and 8R
Class:________________
Name:________________________________
Mrs. Lidowsky, Principal
Mr. Long, Teacher
Date:_____________________
Rotation Notes
Definition: A rotation is when a figure is turned around a certain point.
The time is now 12 o’clock. Both the hour hand (the small hand) and the
minute hand (the big hand) is on 12. The clock at the left will change times.
The clock will become 3 o’clock, then 6 o’clock, then 9 o’clock, and then
back to 12 o’clock. Note that only the hour hand moves and the minute
hand will stay on the 12.
When we move the hour hand from 12 o’clock to 12 o’clock, we moved the
hour hand a whole turn or rotated it 360°.
Note that the time went from
12 o’clock to 3 o’clock. Only
the hour hand moved a quarter
turn clockwise (turn towards
the right). We say the hour
hand rotated 90° clockwise (or
270° counterclockwise, ¾ turn
towards the left).
Note that the time went from
12 o’clock to 6 o’clock. Only
the hour hand moved a half
turn. We say the hour hand
rotated 180°. (Note: You do
not have to say clockwise or
counterclockwise because
going either direction will
cause you end up at the
same position.
TURN OVER FOR MORE NOTES
Note that the time went from
12 o’clock to 9 o’clock. Only
the hour hand moved ¾ of a
turn clockwise (turn towards
the right). We say the hour
hand rotated 270° clockwise
(or 90° counterclockwise, ¼
turn towards the left).
(-2, 4)
Rotation in Coordinate Geometry Notes
NOTE ONE: The blades of the fan are rotating in a counterclockwise direction.
The coordinates of blade M is (4, 2). To move blade M to blade N is to
move blade M 90° counterclockwise to end up at blade N. The coordinates
of blade N is (-2, 4). Note: We went from M(4, 2) to N(-2, 4).
RULES FOR ROTATING A FIGURE 90° COUNTERCLOCKWISE (or 270°
(-4, -2)
(4, 2) clockwise) ABOUT THE ORIGIN:
Switch the coordinates of each point and then multiply the new first
coordinate by –1.
Example: M(4, 2) → N(-2, 4). M(x, y) → N(-y, x)
(SHORT CUT RULE): Switch the x and y. Make the 1st number its
(2, -4)
opposite. Leave the 2nd number alone.
NOTE TWO:
The coordinates of blade M is (4, 2). To move blade M to blade P is to move blade M 180° to end up at blade P. The
coordinates of blade P is (-4, -2). Note: We went from M(4, 2) to P(-4, -2).
RULES FOR ROTATING A FIGURE 180°ABOUT THE ORIGIN:
Multiply both coordinates of each point by –1.
Example: M(4, 2) → P(-4, -2). M(x, y) → P(-x, -y)
(SHORT CUT RULE): (x, y) → (opposite x, opposite y)
NOTE THREE:
The coordinates of blade M is (4, 2). To move blade M to blade Q is to move blade M 90° clockwise to end up at
blade Q. The coordinates of blade Q is (2, -4). Note: We went from M(4, 2) to Q(2, -4).
RULES FOR ROTATING A FIGURE 90° CLOCKWISE (or 270° counterclockwise) ABOUT THE ORIGIN:
Switch the coordinates of each point and then multiply the new second coordinate by –1.
Example: M(4, 2) → Q(2, -4). M(x, y) → Q(y, -x)
(SHORT CUT RULE): Switch the x and y. Make the 2nd number its opposite. Leave the 1st number alone.
ROTATIONAL (or POINT) SYMMETRY: Any figure will look the same after a 360° turn, so a figure must look the
same after a rotation of less than 360° to have rotational symmetry.