Transcript Chapter 9.4 Notes: Perform Rotations

Chapter 9.4 Notes:
Perform Rotations
Goal: You will rotate figures about a point.
• A rotation is a transformation in which a figure is
turned about a fixed point called the center of
rotation.
• Rays drawn from the center of rotation to a point
and its image form the angle of rotation.
• Coordinate Rules for Rotations about the Origin:
Clockwise Rotation:
90o Rotation:
( x, y)  ( y,  x)
Counterclockwise
Rotation:
90o Rotation:
( x, y)  ( y, x)
180o Rotation:
( x, y)  ( x,  y)
180o Rotation:
( x, y)  ( x,  y)
270o Rotation:
( x, y)  ( y, x)
270o Rotation:
( x, y)  ( y,  x)
Ex.1: Graph quadrilateral ABCD with vertices
A(-2, 4), B(-4, -1), C(-3, -3), and D(-1, 0). Then
rotate the quadrilateral 90o clockwise about the
origin.
Ex.2: Graph quadrilateral RSTU with vertices R(3, 1),
S(5, 1), T(5, -3), and U(2, -1). Then rotate the
quadrilateral 270o clockwise about the origin.
• Theorem 9.3 Rotation Theorem:
A rotation is an isometry.
Ex.3:
Ex.4: Find the value of r in the rotation of the triangle.
Ex.5: Graph ΔJKL with vertices J(3, 0), K(4, 3), and
L(6, 0). Rotate the triangle 90o counterclockwise
about the origin.
Ex.6: Graph trapezoid EFGH with vertices E(-3, 2),
F(-3, 4), G(1, 4), and H(2, 2). Then rotate the
trapezoid 180o clockwise about the origin.
Ex.7: Graph trapezoid PQRS with vertices P(2, 5),
Q(4, 4), R(4, -1), and S(2, -2). Then rotate the
trapezoid 270o counterclockwise about the origin.
Ex.8: Graph ΔABC with vertices A(-6, -4), B(-5, -1),
and C(-3, -2). Then rotate the triangle 270o
clockwise about the origin.
Ex.9: