ROTATION.

Rotations in a Coordinate Plane

In a coordinate plane, sketch the quadrilateral whose vertices are A(2, -2), B(4, 1), C(5, 1), and D(5, -1). Then, rotate ABCD 90 counterclockwise about the origin and name the coordinates of the new vertices.

Figure ABCD Figure A’B’C’D’A(2, -2) A’(2, 2)B(4, 1) B’(-1, 4)C(5, 1) C’(-1, 5)D(5, -1) D’(1, 5)

Notice that the x-coordinate of the image is the opposite of the y-coordinate of the preimage. The y-coordinate of the image is the x-coordinate of the preimage.

90 Counterclockwise: (x, y) → (-y, x)90 Clockwise: (x, y) → (y, -x)

Steps in Rotating a Figure

Identify the axis of rotation. Construct a line from each point to the axis of

rotation. Measure the angle. Construct a line from the measured angle to the

axis of rotation. Measure the distance of each point to the axis of

rotation. Use the same measurement in locating the

position of the image in the line made in step 4. Do these to each point of the figure. Connect all the points (image).

Rotate at 180 degrees from the point of origin.

180 Counterclockwise: (x, y) → (-x, -y)

180 Clockwise: (x, y) → (-x,-y)

Rotate at 90 degrees from the point of origin.

90 Counterclockwise: (x, y) → (-y, x)

90 Clockwise: (x, y) → (y, -x)

Tessellation

Learning Target: I can apply transformations (reflection,

translation and rotation) by making a tessellation.

Tessellation A tessellation or tiling of the plane is

a pattern of plane figures that fills the plane with no overlaps and no gaps.

Examples of Tessellation

Examples of Tessellation

Examples of Tessellation

Examples of Tessellation

Steps in making a tesselations

1. Draw a 4 by 4 squares (each square is 2 inches by 2 inches) in a printing paper.

2. Draw one square on top of the paper. On this square draw the pattern of your tessellation.

3. Create your tessellation design by drawing the pattern in the rest of the squares using transformations.

4. Color your tessellation.

Steps in making a tesselations

5. Using your tessellation, identify the following: (Note: To identify location of squares, think of your design as quadrant I of a Cartesian plane.)

a. At least 3 pairs of squares showing reflection.

b. At least 3 pairs of squares showing translation.

c. At least 3 pairs of squares showing rotation.

6. Describe the rule in each transformation.Sample answers for #5 and #6: (1,4) reflected over y-axis

(2,4) (1,1) translated up 1 unit to

(1,2) (1,3) rotated 90 degrees

clockwise to (2,2)

Enjoy the activity!