11.5 Rotations

Rotations

Rotate a Figure 90 about the origin

'( , ) ( , )A x y A y x

Triangle ABC has vertices A(1,2), B(-1,-1) and C (2,0). If the triangle is rotated 90

clockwise about the origin what would the new coordinates be?

x y

A 1 2

B -1 -1

C 2 0

y -x

A’ 2 -1

B’ -1 1

C’ 0 -2

'(2,1), '( 1,1), '(0, 2)A B C

Rotate a figure 180 about the origin

'( , ) ( , )A x y A x y

Triangle ABC has vertices A(-4,-1), B(-2,-5) and C (-2,-1). If the triangle is rotated 180 clockwise about the origin what would the

new coordinates be?x y

A -4 -1

B -2 -5

C -2 -1

-x -y

A’ 4 1

B’ 2 5

C’ 2 1

'(4,1), '(2,5), '(2,1)A B C

Rotate a figure 270 about the origin

'( , ) ( , )A x y A y x

Triangle ABC has vertices A(-2,0), B(-3,5) and C (-1,2). If the triangle is rotated 180

clockwise about the origin what would the new coordinates be?

x y

A -2 0

B -3 5

C -1 2

-y x

A’ 0 -2

B’ -5 -3

C’ -2 -1

'(0, 2), '( 5, 3), '( 2, 1)A B C

Rotational Symmetry

• A figure can be rotated less than 360 degrees about its center so the images matches the original figure

Determine if the star has rotational symmetry. If it does describe the angle of rotation.

• Yes, because the pattern repeats in 5 even intervals.

• The angle of rotation 360/5= 72 degrees.

Homework

• Page 531 (3-6 all and 9-16 all)