an operation that moves or changes a geometric figure (a preimage) in some way to produce a new...

• An operation that moves or changes a geometric figure (a preimage) in some way to produce a new figure (an image).

• Congruence transformations– Changes the position of the figure without changing

the size or shape• Translation• Reflection• Rotation

4.8 Transformations

• The vertices of ABC are A(4, 4), B(6, 6), and C(7, 4). The notation (x, y) → (x + 1, y – 3) describes the translation of ABC to DEF.

• What are the vertices of DEF?

A Translation: moves every point of a figurethe same distance and in the same directionCoordinate notation: (x,y) (x+a,y+b)

• Uses a line of reflection to create a mirror image of the original figure.

• Coordinate notation for reflection in the x-axis : (x ,y) (x , -y)

• Coordinate notation for reflection in the y- axis: (x , y) (-x, y)

A Reflection

• Reflect a figure in the x-axis

Reflection

• Turns a figure about a fixed point called the center of rotation

• Direction: Clockwise or counterclockwise

• Center of rotation: The origin

• Angle: (90˚,180˚,270˚) Angles of rotation formed by rays drawn from the center of rotation through corresponding points on the

pre-image and image

Rotation

• Graph AB and CD. Tell whether CD is a rotation of AB about the origin. If so, give the angle and direction of rotation.

• A(–3, 1), B(–1, 3), C(1, 3), D(3, 1)

Rotation

• Tell whether PQR is a rotation of STR. If so, give the angle and direction of rotation.

Rotations

• Name the type of transformation demonstrated in each picture.

a. b.

c.

Which Transformation?

• A transformation that stretches or shrinks a figure to create a similar figure.

• A figure is reduced or enlarged with respect to a fixed point called the center of dilation.

6.7 Dilations

• The scale factor of a dilation is the ratio of the side length of the image to the corresponding side length of the original figure

• Coordinate notation for a dilation with respect to the origin: (x ,y) ( kx, ky)

• Reduction: 0 < k < 1• Enlargement : k > 1

Dilations

• Draw a dilation of quadrilateral ABCD with vertices A(2, 1), B(4, 1), C(4, – 1), and D(1, – 1). Use a scale factor of 2.

Dilations

Dilations