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Transformations and Coordinate Plane: Homework Solutions, Exercises of Algebra

Manila Central University (MCU)Algebra

Solutions to a geometry homework focusing on transformations, specifically translations, reflections, and dilations, in the context of the coordinate plane. It includes identifying quadrants, plotting and labeling points, and finding the coordinates of images under various transformations.

Typology: Exercises

2021/2022

Uploaded on 08/01/2022

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Name______________________________ Date_______________
Integrated Algebra A
Packet 1
Lesson/Notes
Homework
Coordinate Plane
HW #1
Connecting Points To Make Figures
HW #2
Intro to Transformations/Translations
HW #3
Reflections
HW #4
Symmetry
HW #5
Dilations
HW #6
Review Sheet
Study
Test 1
“Your grades
reflect
your hard work!”
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Download Transformations and Coordinate Plane: Homework Solutions and more Exercises Algebra in PDF only on Docsity!

Name______________________________ Date_______________

Integrated Algebra A

Packet 1

Lesson/Notes Homework

Coordinate Plane HW # Connecting Points To Make Figures HW # Intro to Transformations/Translations HW # Reflections HW # Symmetry HW # Dilations HW # Review Sheet Study Test 1

“Your grades reflect your hard work!”

COORDINATE PLANE

Let’s label the axes, quadrants, and signs on the following grid:

The x-axis is the ___________________ axis.

The y-axis is the ___________________ axis.

Another name for the point (0, 0) is the ____________________.

Using the grid below, let’s plot the following points and label them with the letter:

a) (2, 1) b) (0, 0) c) (-4, 3) d) (-2, -5) e) (1, -3) f) (0, 4) g) (-5, 1) h) (-2, 0)

Give the quadrant each set of coordinates lies in:

a) (1, 5) ________ b) (-2, 4) ________ c) (-3, 2) ________ d) (4, -4) ________

y

x

  • 4 - 2 1 3 5
      • 55
    • 3
    • 1

2

4

  • 5 - 1 4
    • 4

1

  • 5 2
    • 2
  • 3

3

5

Name _____________________________ Date ____________ HW#

  1. Setup the given grid with axes and labels. Label all the quadrants.
  2. Setup the graph with the axes. Graph the following points and label them on the graph with the given letter.

I (0 , 0)

L (3 , 4) O (-6 , 4) V (3 , -2) E (0 , 5)

M (-2 , -1) A (-3 , 0) T (1 , 1) H (0 , -2)

Turn over and complete other side

  1. Graph the points A(1, 1), B(5, 1), C(5, 4). What must be the coordinates of point D if ABCD is a rectangle?

D( , )

  1. Graph the points P(-2,-4) and Q(2,-4). What are the coordinates of R and S if PQRS is a square? (Two answers are possible).

R( , )

S( , )

Review : Write the ordered pairs that correspond to the points labeled A, B, C, and D in the coordinate plane.

1) A( , )

B( , )

C( , )

D( , )

2) A( , )

B( , )

C( , )

D( , )

3) A( , )

B( , )

C( , )

D( , )

Name _____________________________ Date ____________ HW#

Question 1: Which is true of all points in the second quadrant?

(1) positive x-coordinate; positive y-coordinate (2) negative x-coordinate; negative y-coordinate (3) negative x-coordinate; positive y-coordinate (4) positive x-coordinate; negative y-coordinate

Question 2: Which point lies in the third quadrant?

(1) P(0,-5) (2) Q(-5,-11) (3) R(-5,0) (4) T(-5,11)

Question 3: a) Graph and connect the given points: A(1,7), B(1,2), and C(5,2). b) Identify the figure (shape):

c) Find the area of the figure:

Question 4: a) Graph and connect the given points: P(-1,3), Q(5,3), R(5,-2), and S(-1,-2). b) Identify the figure (shape):

c) Find the area of the figure:

Transformation Terms

1) Preimage – _______________________________________________________

_____________________________________________________________________

2) Image – __________________________________________________________

_____________________________________________________________________

3) Transformation – _________________________________________________

_____________________________________________________________________

4) Translation – ______________________________________________________

_____________________________________________________________________

5) Reflection – _______________________________________________________

_____________________________________________________________________

6) Dilation – _________________________________________________________

_____________________________________________________________________

7) Congruent - ______________________________________________________

_____________________________________________________________________

Symmetry Terms

1) Line Symmetry – __________________________________________________

_____________________________________________________________________

2) Point Symmetry - __________________________________________________

_____________________________________________________________________

Translation: a “slide” of the figure

-every point shifts the same distance, in the same direction

  1. a. On the graph, draw and label ΔABC, whose vertices have the coordinates A(1 , 1), B(6 , 2), and C(4 , 4).

b. Under the translation (x , y)(x - 4, y + 2), on the same graph, draw and label ΔABC`.

c. Map the Translation

A(1 , 1)

B(6 , 2)

C(4 , 4)

Another way of notating a translation is with a capital T :

RULE: Ta,b (x , y) = (x + a , y + b)

  1. a. Graph the original triangle and the

image of ΔDEF under the translation T3 , -1.

b. Rewritten as:

c. Map the translation:

D(0 , 2)

E(1 , -3)

F(3 , -1)

  1. Rewrite the translation in a different form:

a. T 2 , 5 - ______________________ b. (x, y)(x + 4, y – 1) - ___________

  1. Does the image remain congruent after a translation? Explain your answer.

Name___________________________ Date_______________

HW#

  1. a. The coordinates of ΔABC are A(0 , -2), B(3 , 1), and C(4 , -3). Graph and label these points.

b. Under the translation (x , y)(x +1, y - 3), draw and label ΔABC`.

c. Map the Translation

  1. a. Graph the image of ΔBUG under the translation T-2 , 4.

b. Map the translation: B(-2 , -3) U(1 , 0) G(3 , -4)

  1. Which of the following is the rule of the translation in which every point moves 6 units to the right on a graph?

a) (x , y)(x , y + 6) b) (x , y)(x +6, y) c) (x , y)(x +6, y + 6) d) (x , y)(x - 6, y)

  1. Which quadrant does the point (-2, 4) lie in? ______

REFLECTIONS [“Flips” or “Mirror”]

LINE REFLECTION :

Pre-image to Image

A → _____

E → _____

D → _____

****Reflection in the Y-axis**** : Plot the following points and connect them, making a triangle.

A (1,2) → A ( )

B (3,4) → B ( )

C (1,5) → C ( )

The ____-coordinate stays the same, while the ____-coordinate is the opposite.

Is a shape congruent after a reflection? __________

A

B

D C

E F

NOTE :

 A reflection like this can also be written as ry-axis.

Name _____________________________ Date ____________ HW#

  1. Graph and write the coordinates of the image of point P(5,-4) under each transformation:

a) a reflection in the x-axis: ( , )

b) a reflection in the y-axis: ( , )

c) a translation that moves the point 3 units to the left and 6 units up: ( , ) [Review from yesterday]

  1. On the grid below, draw  ABC whose vertices are A(1, 1), B(7, 1), and C(4, 5).

a) Draw  ABC , the image of  ABC under a reflection in the y-axis.

b) Write the coordinates of A , B ,and C :

A  ( )

B  ( )

C  ( )

More on next page

  1. Draw rectangle PQRS whose vertices are P(-5,-2), Q(5,-2), R(5, -6), and S(-5, 6). What are the coordinates of the vertices of rectangle PQRS , the image of the original rectangle after a reflection in the x-axis? [Hint: Take each point one at a time!!!]

P ^ (^ )

Q  ( )

R  ( )

S  ( )

  1. Another word for the point (0,0) is the ____________________.
  2. a. A short hint word to describe translations is a “____________”.

b. A short hint word to describe reflections is a “____________”.

  1. Another way of writing “reflection in the y-axis” is _______________.
  2. A shortcut way of writing the following translation: (x, y) (x-1, y+2) is _________.
  3. True or False (circle one): Translations preserve congruence of the original image.
  4. True or False (circle one): Reflections preserve congruence of the original image.

BONUS:

P(1 , 5) x  ^ axis 

r P`( )  3 ,^2 

T

P``( )  y  ^ axis 

r P```( )

Name _____________________________ Date ____________ HW#

  1. Which letter has point symmetry?

a) A b) N c) L d) W

  1. Which letter has line symmetry but not point symmetry?

a) H b) J c) K d) R

  1. Draw all lines of symmetry on the figures below.

a) b) c)

  1. Graph the following points on the given graph.

A (-3, 0) B (6,5) C (0,0) D (-3,3) E (0,-2)

  1. Which quadrant does the point (15, 26) lie in? ________
  2. Rewrite (x, y)(x – 5, y) in another form: __________
  3. What does rx (^) axis stand for when working with transformations? _____________________

DILATIONS

Translations and reflections are transformations that do _________ change the size or shape of a figure [the image is ___________________ to the pre-image].

A dilation is a transformation that changes the size, but not the shape, of a figure. A dilation can “enlarge” or “reduce” a figure. Examples : The eye doctor may put drops in your eyes to dilate your pupils.

Scale Factor : Describes how much a figure is enlarged or reduced. This number is multiplied by the original coordinates (or measurements) to come up with the new coordinates. [ See Examples 1 and 2 below .]

Simple Example :

EXAMPLE 1: Enlargement ( Scale Factor is greater than 1 ):

  1. a. Plot and connect the following points to make  ABC : A(4, 8), B(3, 2), and C(5, 2).

b. Dilate the figure by a scale factor of 2 [notated as D 2 ].

c. List the vertices of the image:

A(4, 8)  A ( )

B(3, 2)  B ( )

C(5, 2)  C ( )

What is the scale factor here? ______