Rigid Transformations

Anything Transformation

100

The original figure is called the ____________ and the transformed figure is known as the ____________

pre image    /     image

200

Transformations such as translations and reflections are called "rigid transformations" because the _______, ________, and ________ remain the same after the transformation

shape, size, angles

300

In coordinate notation, (x, y)-> (x+h, y+k), h represents ___________ shift while k represents __________ shift

horizontal, vertical

400

Point P(9, -4) is translated using the coordinate notation (x,y) -> (x-4, y+7)

What is the location of P'?

P' (5, 3)

500

Triangle A'(5, 6) B'(-4, -5) C'(10, -2) was translated using  (x,y) -> (x-3, y+8)

What is the location of A, B, and C?

A(8, -2)   B(-1, -13)  C(13, -10)

Translations

100

The word we used to describe a translation is ________

slide

200

Translations are an example of a __________ transformation

rigid

300

Translations change the position of an image, but the _________, _________, __________and _________ would never change

size, shape, angles, orientation

400

Triangle Q(8, 10)  R(3, 9)  S(10, 18) is translated using the Vector <-5, 9>

What is the location of Q'R'S'?

Q'(3, 19) R'(-2, 18) S'(5, 27)

500

Quadrilateral P'(6,6) Q'(10,10) R'(-7, -10) S'(-1,0) was translated (x,y) -> (x-9, y)

What is the location of PQRS?

P'(15, 6)  Q(19, 10)  R(2, -10)  S(8, 0)

Vectors

100

Vectors are used for this transformation only

translations

200

Vectors are a quantity with both __________ and __________

direction and magnitude (size)

300

Name the vector that connects a line FROM A(-3, 5) TO B(6, 10)

AB <9,5>

400

Translate triangle W(4, 9) T(-2,9) F(-2, -4):  <-4, -9>

W'(0, 0)  T'(-6, 0)  F'(-6, -13)

500

Rewrite the following translation in proper vector form

(x, y) -> (x-7, y+12)

<-7, 12>

Reflections

100

The word we used in our notes to describe a reflection

flip

200

A reflection across the y axis changes the sign of the ____ coordinates

x 

300

When reflecting points across any line of reflection, the points must remain the same _________ from the line

distance

400

Point B(4, -12) is reflected across the line y = 4. What is the location of B'?

B' (4,20)

500

Reflect triangle A(4,-6) B(-8, 1) C(10,5) across the line y=-x

What are the coordinates of A'B'C'?

A'(6, -4)  B'(-1, 8) C' (-5, -10)

Writing Rules

100

Write a rule in coordinate notation to get point A(-7, 3) to A'(3, -4)

(x,y) -> (x+10, y-7)

200

What reflection happens to get point M(5, -8) to M'(-5, -8)

Reflect across y axis

300

What reflection(s) could get point B(-5,-3) to B'(5,3)

reflect across x and y axis

400

What is the line of reflection if point G(5, 4) is reflected to point G'(-1,4)

x = 2

500

What reflection(s) occurred to get point J(-5,9) to J'(9,-5)

reflect across the line y=x