honeycutt / day 1-tranformation packet
TRANSCRIPT
1
Name___________________________
Transformation Packet
DUE:
TEST:
2
Transformation Vocabulary .
Transformation Related Terms Sketch Reflection
(flip across a line)
Line of reflection
Pre-image and image
Rigid
Rotation
(turn about a point in
a specific direction)
Point of rotation
Degrees
Clockwise or counterclockwise
Rigid Translation
(shifted copy)
Vertical and horizontal shift
Rigid
Dilation
(reduction or
enlargement)
Scale factor
Not rigid
3
Coordinate Transformation Rules
Draw the image of rectangle ABCD under each transformation. Describe the transformation in words! List the
points of the image of rectangle ABCD (the image is called rectangle A’B’C’D ’).
1. (𝑥, 𝑦) → (−𝑥, 𝑦)
2. (𝑥, 𝑦) → (𝑥, −𝑦)
3. (𝑥, 𝑦) → (𝑥 − 3, 𝑦)
4. (𝑥, 𝑦) → (𝑥, 𝑦 + 4)
5. (𝑥, 𝑦) → (𝑥 − 2, 𝑦 − 1)
6. (𝑥, 𝑦) → (𝑦, 𝑥)
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
4
7. (𝑥, 𝑦) → (−𝑦, 𝑥)
8. (𝑥, 𝑦) → (𝑦, −𝑥)
9. (𝑥, 𝑦) → (0.5𝑥, 0.5𝑦)
10. (𝑥, 𝑦) → (−0.5𝑥, −0.5𝑦)
Does the order in which a point is transformed matter?? Let’s see…..
11. (𝑥, 𝑦) → (𝑥 − 2, 𝑦 + 3) → (𝑥, −𝑦)
12. (𝑥, 𝑦) → (𝑥, −𝑦) → (𝑥 − 2, 𝑦 + 3)
What can you infer from examples 11 and 12?
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
A
B
C
D
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
x y
A’
B’
C’
D’
Description:
5
Summary of Coordinate Transformations
Example: Describe the transformation using
coordinate notation.
Example: Find the coordinates of the vertices
of triangle ABC after the transformation
(x,y) (x,-y).
A(–3,4) A’ ( ___,___ )
B(2 , 1)B’ ( ___,___ )
C(–1,–5) C’ ( ___,___ )
Example: Draw ABC with vertices A (4, 0),
B (0, 4), and C (0, 0). Then find the
coordinates of the vertices of the image after
the translation (x, y) → (x–4, y–3), and draw
the image.
Example: Find the coordinates of line
segment AB after the transformation
(x,y) (2x,2y).
A(5,2) A’ ( ___,___ )
B(–8 , –4)B’ ( ___,___ )
6
Rectangle ABCD has coordinates A(1,6),
B(–5,–2), C(–1,–5), and D(5,3).
Graph rectangle ABCD.
Find the length of the four sides of
rectangle ABCD (use the distance
formula).
AB=
BC=
CD=
DA=
Find the area of rectangle ABCD.
Rectangle A’B’C’D’ is the result of
transforming rectangle ABCD based
on the rule (x,y)(2x,2y). What is
the name of this transformation?
Determine the coordinates for
A’B’C’D (use the rule above):
A’= B’=
C’= D’=
Graph A’B’C’D’ on the coordinate
plane at right. Compare the graphs of
ABCD and A’B’C’D’.
Find the length of the four sides of
rectangle A’B’C’D’ (use the distance
formula).
A’B’=
B’C’=
C’D’=
D’A’=
Find the area of rectangle A’B’C’D’.
Compare the side lengths and areas of ABCD and A’B’C’D’. Be specific.
What do you notice about the location of A’B’C’D’ as compared to ABCD?
Hopefully this example will help explain why the LOCATION of a figure changes
under a dilation.
7
In the example on the previous page, you determined the coordinates of A’B’C’D’
after the transformation (x,y)(2x,2y). This transformation is called a
________________________. Recopy the coordinates of A’B’C’D’ below.
A’ B’ C’ D’
Determine the distance of each point above from the origin O(0,0).
OA’ OB’ OC’ OD’
Consider the original coordinates of rectangle ABCD given below.
A(1,6) B(–5,–2) C(–1,–5) D(5,3)
Determine the distance of each point above from the origin O(0,0).
OA OB OC OD
Compare OA and OA’… OB and OB’… OC and OC’…. And OD and OD’.
So a dilation not only changes the length of sides of a figure, but changes the
location of each point making up the figure by….
8
Practice
1. Find the coordinates of the vertices of the image after the specified
transformation, and draw the image.
(x, y) → (x–4, y+2)
(x, y) → (y, −𝑥)
(x, y) → (0.5x, 0.5𝑦)
2. Transformations can be used to show motion. Use coordinate notation to
describe the transformation of the drummer from one picture to the next
picture.
3. Draw one triangle with vertices (2, 1), (3, 4), and
(4, 1) and a second triangle with vertices (4, 1), (3,
4), and (2, 1).Describe two different
transformations that could move the first triangle
onto the second.
9
4. The vertices of quadrilateral ABCD are A(3, 4), B(2, 4), C(3, 2), and D(4, 1).
After a translation, the coordinates of A’ are (5, 1). Describe the translation
using coordinate notation. Then find the coordinates of B’, C’, and D’.
5. Determine whether or not the following statements are TRUE or FALSE.
a. _____The transformation (x,y) (x+2, y+2) applied to the ordered pairs
that form a square will result in a square that covers twice the area of the
original square.
b. _____The transformation (x,y)(x,y-2) will translate a figure left 2
units.
c. _____When reflected over the x-axis, the point (3,–5) becomes (3,5).
d. _____When reflected over the y-axis, the point (3, –5) becomes (3,5).
e. _____ If square ABCD has A(–4,1) and is rotated 90° clockwise about
the origin, then the new coordinates of A must be (1,4).
f. _____Translating a figure results in a figure similar, but not congruent to
the original figure.
g. _____ Rotating a figure results in a figure congruent to the original
figure.
h. _____The only transformation that results in a figure similar, but not
congruent to the original figure is a dilation.
6. MULTIPLE CHOICE
Rectangle A′B′C′D′ is the image of rectangle
ABCD after which of the following rotations?
A. A 90° clockwise rotation about the origin
B. A 90° counterclockwise rotation about the origin
C. A 180° rotation about the origin
D. A reflection over the y-axis.
10
7. The vertices of triangle ABC are
A(–3,–1), B(–4,3), and C(1,2).
Reflect the triangle over the line
𝑦 = 𝑥. Graph the triangle and its
image.
8. The vertices of quadrilateral ABCD
are A(5,–2), B(7,–4), C(4,–7), and
D(2,–5). Rotate the figure 90°
counterclockwise. Graph the figure and
its image.
8. In the diagram, the quadrilateral is
rotated about P. What is the value
of y?
9. Graph ∆DEF with vertices D(0,3),
E(4,3), and F(0,6). Then graph its
image after translating according to the
rule (x,y) (x, y+2), then rotating 180°.
11
NC FINAL Practice 1. Which rotation will carry a square onto itself?
a. 30° clockwise rotation
b. 45°counterclockwise rotation
c. 60° clockwise rotation
d. 90° counterclockwise rotation
2. Which rotation will carry a regular hexagon onto
itself?
a. 30° clockwise rotation
b. 90°counterclockwise rotation
c. 120° clockwise rotation
d. 330° counterclockwise rotation
3. Which rotation will carry a regular octagon onto
itself?
a. 30° counterclockwise rotation
b. 120°counterclockwise rotation
c. 135° clockwise rotation
d. 300° clockwise rotation
4. Which rotation will carry a regular decagon onto
itself?
a. 45° clockwise rotation
b. 72°counterclockwise rotation
c. 90° clockwise rotation
d. 148° counterclockwise rotation
5. If triangle ABC is translated 5 units down and 3
units left, which transformation would move it back
to its original location?
a. (𝑥, 𝑦) → (𝑥 + 3, 𝑦 + 5)
b. (𝑥, 𝑦) → (𝑥 − 3, 𝑦 − 5)
c. (𝑥, 𝑦) → (𝑥 + 5, 𝑦 + 3)
d. (𝑥, 𝑦) → (𝑥 − 5, 𝑦 − 3)
6. If triangle ABC is rotate 90° clockwise, which
transformation would move it back to its original
location?
a. (𝑥, 𝑦) → (−𝑥, −𝑦)
b. (𝑥, 𝑦) → (𝑦, −𝑥)
c. (𝑥, 𝑦) → (−𝑦, 𝑥)
d. (𝑥, 𝑦) → (−𝑦, −𝑥)
7. 𝑀𝑁̅̅ ̅̅ ̅ has 𝑀(1,9) and 𝑁(5,12). If 𝑀𝑁̅̅ ̅̅ ̅ is dilated with respect to the origin by a scale factor of k to produce
𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅, which statement must be true?
a. 𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅ has a length of 5.
b. The midpoint of 𝑀′𝑁′̅̅ ̅̅ ̅̅ ̅ is (3,10.5).
c. The line that passes through 𝑀′ and 𝑁′ has a slope of (3
4) 𝑘.
d. The line that passes through 𝑀′ and 𝑁′ intersects the y-axis at (0,8.25𝑘).
8. Triangle EGF is graphed below. Triangle EGF will be rotated 90° clockwise around the origin and will then
be reflected across the y-axis, producing an image triangle. Which additional transformation will map the image
triangle back onto the original triangle?
A rotation 270° counterclockwise around the origin
B rotation 180° counterclockwise around the origin
C reflection across the line y = − x
D reflection across the line y = x
12