Transformations

Math 8

Four Types• Translation (Slide)• Rotation (turn)• Reflection (flip)• Dilation (shrinking/stretching)

Examples:

When working with transformations it is helpful to

remember the coordinate systemQuadrant 1 (+x, +y)Quadrant 2 (-x, +y)Quadrant 3 (-x, -y) Quadrant 4 (+x, -y)

Examples:

Reflections-(Flip)When you reflect a shape in the coordinate plane, you reflect it over a line. This line is called the line of reflection/symmetry.

When a figure is reflected on a coordinate plane, every point of the figure must have a corresponding point on the other side.

Most reflections are over the x-axis (horizontal), the y-axis (vertical), or the line y = x (diagonal uphill from left to right.)

ReflectionsWhen you reflect a shape over the x –axis, use the same coordinates and multiply the y coordinate by –1. (x, opposite y)

When you reflect a shape over the y-axis, use the same coordinates and multiply the x coordinate by –1. (opposite x, y)

When you reflect a shape over the line y=x, use the same coordinates and multiply both by –1.

Examples:

1. Reflect the triangle over the x-axis and y – axis.

Examples:

Examples:

Translations (Slides/Glide)

To translate a figure in the direction describe by an ordered pair, add the ordered pair to the coordinates of each vertex of the figure.The new set of ordered pairs is called the image. It is shown by writing A’. This is read the image of point A.

ExamplesFind the coordinates of the vertices of each figure after the translation described. Use the graph to help you.

Examples:

Find the coordinates of the vertices of each figure after the translation described.

Rotations (Turns)   ¼ turn = 90 degrees rotation   ½ turn = 180 degrees rotation ¾ turn = 270 degrees rotation   full turn = 360 degrees rotation

Example:

Example:

In the coordinate plane we have 4 quadrants. If the shape is rotated around

(0,0) then:90 degrees rotation moves 1 quadrant

Rotating 90 clockwise. (x, y) (y, opposite x) same as 270 counterclockwise. Rotating 90 counterclockwise is the same as 270 clockwise. (x, y) (opposite y, x)

180 degrees rotation moves 2 quadrants Multiply both by – 1. (x, y,)  (opposite x, opposite y)

270 degrees rotation moves 3 quadrants Rotating 270 counterclockwise is the same as 90

clockwise (x, y) (y, opposite x)

360 degrees rotation moves 4 quadrants (stays the same)

Examples:

If a triangle is in Quadrant 2 and is rotated 270 counterclockwise, what quadrant is it now in?If a triangle is in Quadrant 4 and is rotated 90 clockwise, what quadrant is it now in?

SymmetryTwo Types:1. Line Symmetry (can

be called reflectional symmetry)– if you can fold a shape and have the edges meet

The place where you fold is called the line of symmetry

More Line Symmetry

InkBlots

Does the Human Face Possess Line Symmetry?

Answer: No

Girl

Carpets

Examples:Do the following shapes have line symmetry? If so, how many lines of symmetry do they have?

a. b. c. d. e.

Rotational Symmetry2. Rotational Symmetry: If you can turn the shape less than 360o and still have the same shape.Order of Rotational Symmetry: Is the

number of rotations that must be made to return to the original orientation

Minimum Rotational Symmetry: The smallest number of degrees a shape can be rotated and fit exactly on itself

Hint: Take 360o divided by the number of sides/points.

Examples:

Examples:

Does the following shape have rotational symmetry? If yes, what is the order and MRS?

a. b. c. d. e.