Congruence & Similarity

Translations

100

What is a translation?

A transformation that slides a figure along a straight line. The image has the same shape and size as the pre-image.

200

What is the rule for translation?

(x,y) = (x + j, y + k)

300

What is the rule for translations in arrow notation if you slide right 2 units and slide down 3 units?

(x + 2, y - 3) 

or 

(x + 2, y + (-3))

400

What is the image of (-4, 5) after you translate it right 7 units and down 6 units?

(3, -1)

500

What is the translation if you...

slide A (-2, -5) --> A' (7, -2)

Slide/Shift 9 units to the right and 3 units up

Reflections

100

What is a reflection?

A transformation that flips a figure across a line called the line of reflection. Each point and its image are the same distance from the line of reflection. The image has the same shape and size as the pre-image.

200

What are the rules for reflection?

Reflection over the x-axis is (x,y) --> (x, -y)

Reflection over the y-axis is (x,y) --> (-x, y)

300

What is the image of (-6, 3) after you reflect it across the x-axis?

(-6,-3)

400

What is the image of (7,-2) after you reflect it across the y-axis?

(-7,-2)

500

What is the image of (-8,-1) after you reflect it across the x-axis and then the y-axis?

(8,1)

Rotations

100

What is a rotation?

A transformation that turns a figure around a given point called the center of rotation. The image has the same shape and size as the pre-image.

200

What are the rules of rotation?

90^o counterclockwise (270^o clockwise) 

                 (x,y) --> (-y,x)

180^o          (x,y) --> (-x,-y)

270^o counterclockwise (90^o clockwise)

                 (x,y) --> (y,-x)

300

What is the image of (-8, -3) after you rotate it 180^o?

(8,3)

400

What is the image of (1, 9) after you rotate it 90^o counterclockwise?

(-9,1)

500

What is the image of (-4,-6) after you rotate it 270^o clockwise?

(6,-4)

Dilation

100

What is a dilation?

A transformation that enlarges or shrinks a figure from a given point. It creates a similar figure. A dilation is created by multiplying a scale factor by each coordinate.

200

What are the 2 types of dilations?

Enlargement and Reduction

300

How do you know if the image is larger than the pre-image?

How do you know if the image is smaller than the pre-image?

The image is larger than the pre-image if the scale factor is greater than 1.

The image is smaller than the pre-image if the scale factor is greater than 0 but less than 1.

400

What is the image of (-3,8) after you dilate it with a scale factor of 3?

(-9,24)

500

Find the scale factor between 

A(16,-8) --> A'(4,-2)

B(12,-4) --> B'(3,-1)

C(8,0)    --> C'(2,0)

1/4

Congruence VS Similarity

100

What is the difference between similarity and congruence?

Congruence has the same shape and size, regardless of position/orientation.

Similarity has the same shape but not the same size.

200

If you rotate, translate, and reflect an image from its pre-image, is it congruent or similar?

Congruent

300

Which transformation changes figures from being congruent to being similar?

Dilation.

400

Triangle ABC is reflected, rotated, then dilated by a scale factor of 1/3.  Will this shape be similar, congruent or both?

What is similar.

500

Rectangle QUAD has coordinates Q(2,5), U(2,8), A(7,8), and D(7,5). 

Q'U'A'D' is the image of QUAD after a dilation with center (0,0) and scale factor 4. 

What are the coordinates of point A'?

A' (28, 32)