translations- a transformation in which each point of a figure moves the same
______ and in the same ______, the
corresponding angles are ______ and the corresponding sides are ______.
look at the graph below. record the coordinate pairs for the pre - image. when a
point has been transformed it is labeled with a symbol called ______. for
example a ______, b ______ c ______ if two transformations have been
performed it is called ______.
pre - image (original
image)
a ( , )
b ( , )
c ( , )
translation rule
(x + 5, y + 2)
a ( , )
b ( , )
c ( , )
in words, describe the translation:
translation rule
(x + 8, y - 8)
a ( , )
b ( , )
c ( , )
(graph of a triangle with points a, b, c and another graph of a quadrilateral with points q, r, s, t and their transformed versions)
sometimes you are given a graph and
asked “what is the coordinate notation”?
ex: count the spaces move across and
up to get to the new point
check it: preimage
q ( , ) q ( , )
r ( , ) r ( , )
s ( , ) s ( , )
t ( , ) t ( , )

Question

translations- a transformation in which each point of a figure moves the same
______ and in the same ______, the
corresponding angles are ______ and the corresponding sides are ______.
look at the graph below. record the coordinate pairs for the pre - image. when a
point has been transformed it is labeled with a  symbol called ______. for
example a ______, b ______ c ______ if two transformations have been
performed it is called ______.
pre - image (original
image)
a (  ,  )
b (  ,  )
c (  ,  )
translation rule
(x + 5, y + 2)
a (  ,  )
b (  ,  )
c (  ,  )
in words, describe the translation:
translation rule
(x + 8, y - 8)
a (  ,  )
b (  ,  )
c (  ,  )
(graph of a triangle with points a, b, c and another graph of a quadrilateral with points q, r, s, t and their transformed versions)
sometimes you are given a graph and
asked “what is the coordinate notation”?
ex: count the spaces move across and
up to get to the new point
check it: preimage
q (  ,  ) q (  ,  )
r (  ,  ) r (  ,  )
s (  ,  ) s (  ,  )
t (  ,  ) t (  ,  )

Accepted Answer

### Part 1: Filling in the Blanks about Translations
#### Explanation for Translations Definition:
A translation is a transformation where each point of a figure moves the same **distance** and in the same **direction**. In a translation, corresponding angles are **congruent** (equal in measure) and corresponding sides are **congruent** (equal in length) because translations preserve the shape and size of the figure.

#### Explanation for Transformed Points:
When a point is transformed, it is labeled with a `'` symbol called a **prime** (e.g., $ A' $ is read as "A prime"). If two transformations are performed, the image is called a **double prime** (e.g., $ A'' $).

### Part 2: Coordinates for the Pre - Image (Triangle $ ABC $)
To find the coordinates of the pre - image, we look at the graph. Let's assume the grid has the origin $(0,0)$ at the intersection of the x - and y - axes.
- Point $ A $: Looking at the graph, if we count the units from the origin, let's say $ A $ is at $(-9, 5)$ (we move 9 units left on the x - axis (negative x - direction) and 5 units up on the y - axis).
- Point $ B $: $ B $ is directly below $ A $, so it has the same x - coordinate as $ A $ and a lower y - coordinate. So $ B $ is at $(-9, 1)$.
- Point $ C $: $ C $ is to the right of $ B $, so it has the same y - coordinate as $ B $ and a larger x - coordinate. So $ C $ is at $(-5, 1)$.

### Part 3: Applying the First Translation Rule $(x + 5, y+2)$
The translation rule $(x + 5, y + 2)$ means we add 5 to the x - coordinate and 2 to the y - coordinate of each pre - image point.
- For $ A(-9, 5) $:
  New x - coordinate: $-9+5=-4$
  New y - coordinate: $5 + 2=7$
  So $ A'(-4, 7) $
- For $ B(-9, 1) $:
  New x - coordinate: $-9+5=-4$
  New y - coordinate: $1+2 = 3$
  So $ B'(-4, 3) $
- For $ C(-5, 1) $:
  New x - coordinate: $-5+5 = 0$
  New y - coordinate: $1+2=3$
  So $ C'(0, 3) $

### Part 4: Describing the Translation $(x + 5, y + 2)$
In words, the translation $(x + 5, y+2)$ means the figure is moved **5 units to the right** (because we add 5 to the x - coordinate) and **2 units up** (because we add 2 to the y - coordinate).

### Part 5: Applying the Second Translation Rule $(x + 8, y-8)$ to $ A', B', C' $
We apply the rule $(x + 8, y - 8)$ to the coordinates of $ A', B', C' $.
- For $ A'(-4, 7) $:
  New x - coordinate: $-4+8 = 4$
  New y - coordinate: $7-8=-1$
  So $ A''(4, -1) $
- For $ B'(-4, 3) $:
  New x - coordinate: $-4+8 = 4$
  New y - coordinate: $3-8=-5$
  So $ B''(4, -5) $
- For $ C'(0, 3) $:
  New x - coordinate: $0+8 = 8$
  New y - coordinate: $3-8=-5$
  So $ C''(8, -5) $

### Final Answers (Filled Blanks and Coordinates)

#### Translations Definition Blanks:
- distance, direction, congruent, congruent

#### Transformed Points Blanks:
- prime, $ A' $, $ B' $, $ C' $, double prime

#### Pre - Image Coordinates:
- $ A(-9, 5) $, $ B(-9, 1) $, $ C(-5, 1) $

#### First Translation ($x + 5, y + 2$) Coordinates:
- $ A'(-4, 7) $, $ B'(-4, 3) $, $ C'(0, 3) $

#### Translation Description:
- 5 units to the right and 2 units up

#### Second Translation ($x + 8, y - 8$) Coordinates:
- $ A''(4, -1) $, $ B''(4, -5) $, $ C''(8, -5) $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Part 1: Filling in the Blanks about Translations

Part 2: Coordinates for the Pre - Image (Triangle \( ABC \))

Part 3: Applying the First Translation Rule \((x + 5, y+2)\)

Part 4: Describing the Translation \((x + 5, y + 2)\)

Part 5: Applying the Second Translation Rule \((x + 8, y-8)\) to \( A', B', C' \)

Final Answers (Filled Blanks and Coordinates)

Translations Definition Blanks:

Transformed Points Blanks:

Pre - Image Coordinates:

First Translation (\(x + 5, y + 2\)) Coordinates:

Translation Description:

Second Translation (\(x + 8, y - 8\)) Coordinates:

Answer: