3. use the graph shown to complete each statement below
a. give a verbal description of the transformation
(handwritten: reflection over the y - axis)
b. give an algebraic representation of the transformation
(handwritten: (x,y)→(-x,y))
c. list which of the following changed or stayed the same:
- size of the figure:
- orientation of the figure:
- orientation of the vertices:

4. bella believes the graph shows a translation down while
scott believes it shows a reflection over the x - axis. who is
correct? explain.

5. triangle abc has the coordinates shown in the table. miguel
is going to reflect the triangle using the rule (x, y) → (-x, y).
a. what is the line of reflection?
b. list the coordinates of the image in the table. in which
quadrant will the image lie?

in 6 - 8, use the description to identify the line of reflection and write an algebraic representation
for the reflection.

| 6. point a(8, -1) is reflected to a(-8, -1). | 7. a figure is reflected from quadrant i to iv. | 8. point z(-5, 7) is reflected to z(-5, -7). |
| --- | --- | --- |
| line of reflection | | |
| algebraic representation | | |

summarize today’s lesson:

Question

3. use the graph shown to complete each statement below
   a. give a verbal description of the transformation
      (handwritten: reflection over the y - axis)
   b. give an algebraic representation of the transformation
      (handwritten: (x,y)→(-x,y))
   c. list which of the following changed or stayed the same:
      - size of the figure:
      - orientation of the figure:
      - orientation of the vertices:

4. bella believes the graph shows a translation down while
   scott believes it shows a reflection over the x - axis. who is
   correct? explain.

5. triangle abc has the coordinates shown in the table. miguel
   is going to reflect the triangle using the rule (x, y) → (-x, y).
   a. what is the line of reflection?
   b. list the coordinates of the image in the table. in which
      quadrant will the image lie?

in 6 - 8, use the description to identify the line of reflection and write an algebraic representation
for the reflection.

| 6. point a(8, -1) is reflected to a(-8, -1). | 7. a figure is reflected from quadrant i to iv. | 8. point z(-5, 7) is reflected to z(-5, -7). |
| --- | --- | --- |
| line of reflection |  |  |
| algebraic representation |  |  |

summarize today’s lesson:

Accepted Answer

### Problem 3 (Top Graph)
# Explanation:
## Step1: Describe transformation verbally
The figure is reflected over the y-axis.
## Step2: Write algebraic rule
For reflection over y-axis: $(x,y)
ightarrow (-x,y)$
## Step3: Analyze size change
Size stays the same (congruent figures).
## Step4: Analyze figure orientation
Orientation is reversed (mirror image).
## Step5: Analyze vertex orientation
Vertex order is reversed (mirror direction).
# Answer:
a. Verbal description: Reflection over the y-axis
b. Algebraic representation: $(x,y)
ightarrow (-x,y)$
c. - Size of the figure: Stayed the same
   - Orientation of the figure: Changed (reversed)
   - Orientation of the vertices: Changed (reversed)

---

### Problem 4 (Middle Graph)
# Brief Explanations:
A translation down would shift all points vertically without flipping the figure. A reflection over the x-axis flips the figure across the x-axis, reversing the sign of the y-coordinates. The graph shows the figure is flipped (not just shifted), matching a reflection over the x-axis.
# Answer:
Scott is correct. The figure is flipped across the x-axis (y-coordinates are negated), which matches a reflection over the x-axis, not a downward translation (which would not flip the figure).

---

### Problem 5
# Explanation:
## Step1: Identify reflection line
Rule $(x,y)
ightarrow (-x,y)$ matches reflection over y-axis.
## Step2: Calculate image coordinates
Apply rule to each point:
$A(-4,-6)
ightarrow (4,-6)$
$B(-5,-8)
ightarrow (5,-8)$
$C(-1,-3)
ightarrow (1,-3)$
## Step3: Identify quadrant
Points with positive x, negative y lie in Quadrant IV.
# Answer:
a. Line of reflection: The y-axis (x=0)
b. Image coordinates:
$A'(4, -6)$
$B'(5, -8)$
$C'(1, -3)$
The image lies in Quadrant IV.

---

### Problems 6-8
# Explanation:
## Step6: Analyze point A reflection
$A(8,-1)
ightarrow A'(-8,-1)$: x-coordinate negated, y stays. This is reflection over y-axis.
## Step7: Analyze quadrant reflection
Reflection from Quadrant I (+x,+y) to IV (+x,-y) negates y-coordinate, so reflection over x-axis.
## Step8: Analyze point Z reflection
$Z(-5,7)
ightarrow Z'(-5,-7)$: y-coordinate negated, x stays. This is reflection over x-axis.
# Answer:
| LINE OF REFLECTION | 6. y-axis (x=0) | 7. x-axis (y=0) | 8. x-axis (y=0) |
|---------------------|-----------------|-----------------|-----------------|
| ALGEBRAIC REPRESENTATION | $(x,y)
ightarrow (-x,y)$ | $(x,y)
ightarrow (x,-y)$ | $(x,y)
ightarrow (x,-y)$ |

---

### Summarize today's lesson:
# Brief Explanations:
The lesson covers reflections, a type of rigid transformation that flips a figure across a line (x-axis, y-axis, etc.). Key topics include identifying reflections from graphs, writing algebraic rules for reflections, analyzing how reflections affect figure size/orientation, and linking reflection rules to coordinate changes.
# Answer:
Today's lesson focused on **reflections (rigid transformations)**:
- Identifying reflections from graphs and verbal descriptions
- Writing algebraic rules for reflections over the x-axis ($(x,y)
ightarrow (x,-y)$) and y-axis ($(x,y)
ightarrow (-x,y)$)
- Analyzing that reflections preserve figure size but reverse orientation
- Matching reflection rules to coordinate changes and quadrant shifts

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 3 (Top Graph)

Step1: Describe transformation verbally

Step2: Write algebraic rule

Step3: Analyze size change

Step4: Analyze figure orientation

Step5: Analyze vertex orientation

Step1: Identify reflection line

Step2: Calculate image coordinates

Step3: Identify quadrant

Answer:

Problem 4 (Middle Graph)