Coordinate Reflections Study Guide
Module 2 • Geometry | CCSS 8.G.A.3
Name: Date: Period:
Coordinate Plane Reflections
Part I: Quick Rules & Reflections of Points and Figures over Coordinate Axes
Reflection Quick Rules
Tip: The axis named keeps its value!
Across y-axis (Horizontal) (x, y) → (−x, y)
Across x-axis (Vertical) (x, y) → (x, −y)
Directions: Find the image coordinates after each given reflection. Use the grid lines to count units, apply the algebraic rule to each point or vertex, and select the correct answer.
1 Reflect Point across y-axis
M(−2, 4)
x y 4 -4 4 -4 M
A M′(−2, −4)
B M′(2, −4)
C M′(2, 4)
D M′(−4, 2)
2 Reflect Point across x-axis
G(3, 2)
x y 4 -4 4 -4 G
A G′(−3, 2)
B G′(3, −2)
C G′(−3, −2)
D G′(2, 3)
3 Reflect Segment AB across y-axis
A(−4, 1), B(−1, 3)
x y A B
A A′(−4, −1), B′(−1, −3)
B A′(4, −1), B′(1, −3)
C A′(1, 4), B′(3, 1)
D A′(4, 1), B′(1, 3)
4 Reflect ΔDEF across x-axis
D(1,−2), E(4,−2), F(1,−4)
x y D E F
A D′(1, 2), E′(4, 2), F′(1, 4)
B D′(−1, −2), E′(−4, −2), F′(−1, −4)
C D′(−1, 2), E′(−4, 2), F′(−1, 4)
D D′(2, 1), E′(2, 4), F′(4, 1)
Module 2: Transformations & Coordinate Geometry Page 1 of 4 • Points & Figures over Axes
Module 2 • Geometry | Extension & Mastery
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Reflections over Specific Lines
Part II: Vertical Lines (x = k) and Horizontal Lines (y = k)
How to Reflect Across Any Line
Count grid units straight from each vertex to the reflection line; count the exact same distance across.
Preservation Property Distance to line is preserved!
Directions: The red dashed line (−−−) represents the line of reflection. Use the visible grid lines to count units for each point or figure.
5 Reflect Point across line x = 1
A(−2, 3)
x=1 x y A
A A′(2, 3)
B A′(−2, −1)
C A′(4, 3)
D A′(3, −2)
6 Reflect ΔTUV across y = 2
T(1,−1), U(4,−1), V(1,1)
y=2 x y T U V
A T′(1, 1), U′(4, 1), V′(1, −1)
B T′(3, −1), U′(0, −1), V′(3, 1)
C T′(1, −5), U′(4, −5), V′(1, −3)
D T′(1, 5), U′(4, 5), V′(1, 3)
7 Reflect Point across line y = 1
C(2, −3)
y=1 x y C
A C′(2, −1)
B C′(2, 5)
C C′(−2, −3)
D C′(2, −5)
8 Reflect Segment GH across x = −1
G(1,−3), H(2,−1)
x=-1 x y G H
A G′(−1, −3), H′(−2, −1)
B G′(1, 3), H′(2, 1)
C G′(−3, −3), H′(−4, −1)
D G′(−3, 3), H′(−4, 1)
Module 2: Transformations & Coordinate Geometry Page 2 of 4 • Specific Reflection Lines
Module 2 • Geometry | Multi-Vertex Polygons
Name:
Reflections of Geometric Figures
Part III: Transforming Polygons Vertex-by-Vertex with Full Coordinate Proofs
Figure Strategy: Reflect each vertex using algebraic rules, record in the table, and connect points.
Size & Shape are Preserved (≅)
9 Reflect Triangle ΔABC across y-axis
Rule: (x, y) → (−x, y)
x y A B C
| Vertex |
Pre-Image |
Transformed Image |
| A |
(1, 2) |
A′( , ) |
| B |
(4, 2) |
B′( , ) |
| C |
(1, 5) |
C′( , ) |
A A′(−1, 2), B′(−4, 2), C′(−1, 5)
B A′(1, −2), B′(4, −2), C′(1, −5)
C A′(−1, −2), B′(−4, −2), C′(−1, −5)
D A′(2, 1), B′(2, 4), C′(5, 1)
10 Reflect Quadrilateral RSTU across x-axis
Rule: (x, y) → (x, −y)
x y R S T U
| Vertex |
Pre-Image |
Transformed Image |
| R |
(−4, −1) |
R′( , ) |
| S |
(−1, −1) |
S′( , ) |
| T |
(−2, −4) |
T′( , ) |
| U |
(−4, −4) |
U′( , ) |
A R′(4, −1), S′(1, −1), T′(2, −4), U′(4, −4)
B R′(4, 1), S′(1, 1), T′(2, 4), U′(4, 4)
C R′(−1, −4), S′(−1, −1), T′(−4, −2), U′(−4, −4)
D R′(−4, 1), S′(−1, 1), T′(−2, 4), U′(−4, 4)
11 Reflect Triangle ΔMNP across line y = 1
Line: y = 1
y=1 x y M N P
| Vertex |
Pre-Image |
Transformed Image |
| M |
(1, 2) |
M′( , ) |
| N |
(4, 2) |
N′( , ) |
| P |
(1, 4) |
P′( , ) |
A M′(1, −2), N′(4, −2), P′(1, −4)
B M′(1, 0), N′(4, 0), P′(1, −2)
C M′(−1, 2), N′(−4, 2), P′(−1, 4)
D M′(0, 1), N′(0, 4), P′(−2, 1)
Module 2: Transformations & Coordinate Geometry Page 3 of 4 • Multi-Vertex Polygons
Module 2 • Geometry | Line Detection & Analysis
Name:
Detecting Lines of Reflection
Part IV: Transforming Polygons across Specific Lines & Identifying Reflection Line Equations
Directions: Apply reflection rules across specific lines to calculate transformed coordinates, or count distances between figures to identify the exact equation for the line of reflection.
12 Reflect ΔJKL across x = 1
x=1 x y J K L
A J′(−2, 1), K′(−4, 1), L′(−2, 4)
B J′(2, −1), K′(4, −1), L′(2, −4)
C J′(0, 1), K′(−2, 1), L′(0, 4)
D J′(1, 2), K′(1, 4), L′(4, 2)
13 Detect Line: Fig 1 → Fig 2
x y Fig 1 Fig 2
A Line y = 1
B Line y = 2
C Line x = 1
D x-axis (y = 0)
14 Reflect ΔPQR across y = −1
y=-1 x y P Q R
A P′(1, −1), Q′(4, −1), R′(1, −3)
B P′(1, −3), Q′(4, −3), R′(1, −5)
C P′(−1, 1), Q′(−4, 1), R′(−1, 3)
D P′(1, 0), Q′(4, 0), R′(1, −2)
15 Detect Line: Fig 1 → Fig 2
x y Fig 1 Fig 2
A y-axis (x = 0)
B Line x = 1
C Line x = 2
D Line y = 1
Module 2: Transformations & Coordinate Geometry Page 4 of 4 • Line Detection & Analysis
Coordinate Reflections Answer Key
Module 2 • Geometry | Teacher Answer Key
CCSS 8.G.A.3 | Part I Key (Q1–Q4)
Coordinate Reflections — Answer Key
Part I: Quick Rules & Reflections of Points and Figures over Coordinate Axes
Part I Quick Keys:
Q1: C Q2: B Q3: D Q4: A
1 Reflect M(−2, 4) over y-axis
CORRECT: C
M M′(2, 4)
Algebraic Rule: (x, y) → (−x, y)
−(−2) = 2, while y remains 4 → M′(2, 4).
Distractors: B reflects over origin; D swaps coordinates.
2 Reflect G(3, 2) over x-axis
CORRECT: B
G G′(3, −2)
Algebraic Rule: (x, y) → (x, −y)
Keep x = 3, negate y: −(2) = −2 → G′(3, −2).
Distractors: A reflects over y-axis; C reflects over origin.
3 Reflect Segment AB over y-axis
CORRECT: D
A′(4, 1) B′(1, 3)
Rule: (−x, y) applied to both endpoints:
A(−4, 1) → A′(4, 1); B(−1, 3) → B′(1, 3).
Verification: Pre-image and image segments are congruent (≅).
4 Reflect ΔDEF over x-axis
CORRECT: A
D′ E′ F′
Rule: (x, −y) applied to vertices:
D′(1, 2), E′(4, 2), F′(1, 4).
Vertical reflection across y = 0 preserves orientation & size.
Module 2: Transformations & Coordinate Geometry Page 1 of 4 • Part I Detailed Solutions
Module 2 • Geometry | Teacher Answer Key
CCSS 8.G.A.3 | Part II Key (Q5–Q8)
Reflections over Specific Lines — Answer Key
Part II: Vertical Lines (x = k) and Horizontal Lines (y = k)
Part II Quick Keys:
Q5: C Q6: D Q7: B Q8: C
5 Reflect A(−2, 3) over x = 1
CORRECT: C
x=1 A A′(4, 3)
Step 1: Distance from x = −2 to x = 1 is 3 units right.
Step 2: Count 3 units right of x = 1: 1 + 3 = 4 → A′(4, 3).
The y-value is completely unchanged.
6 Reflect ΔTUV over y = 2
CORRECT: D
y=2 T′ U′ V′
T, U have y = −1 (3 below y = 2) → reflect to y = 2 + 3 = 5.
V has y = 1 (1 below y = 2) → reflects to y = 2 + 1 = 3.
T′(1, 5), U′(4, 5), V′(1, 3)
7 Reflect C(2, −3) over y = 1
CORRECT: B
y=1 C C′(2, 5)
Pre-image y = −3 is 4 units below y = 1.
Reflect 4 units above line: 1 + 4 = 5.
C′(2, 5)
8 Reflect GH over x = −1
CORRECT: C
x=-1 G′ H′
G(1,−3) is 2 units right → image is 2 units left: x = −3.
H(2,−1) is 3 units right → image is 3 units left: x = −4.
G′(−3, −3), H′(−4, −1)
Module 2: Transformations & Coordinate Geometry Page 2 of 4 • Part II Detailed Solutions
Module 2 • Geometry | Teacher Answer Key
CCSS 8.G.A.3 | Part III Key (Q9–Q11)
Multi-Vertex Polygons — Answer Key & Completed Tables
Part III: Transforming Polygons Vertex-by-Vertex with Full Coordinate Proofs
Part III Quick Keys:
Q9: A Q10: D Q11: B
9 Reflect ΔABC across y-axis
Rule: (x, y) → (−x, y) CORRECT: A
A′ B′ C′
| Vertex |
Pre-Image |
Transformed Image (Solution) |
| A |
(1, 2) |
A′(−1, 2) |
| B |
(4, 2) |
B′(−4, 2) |
| C |
(1, 5) |
C′(−1, 5) |
Each vertex reflects horizontally across the y-axis. The base length (3 units) and height (3 units) are fully preserved.
10 Reflect Quadrilateral RSTU across x-axis
Rule: (x, y) → (x, −y) CORRECT: D
R′ S′ T′ U′
| Vertex |
Pre-Image |
Transformed Image (Solution) |
| R |
(−4, −1) |
R′(−4, 1) |
| S |
(−1, −1) |
S′(−1, 1) |
| T |
(−2, −4) |
T′(−2, 4) |
| U |
(−4, −4) |
U′(−4, 4) |
Quadrilateral moves from Quadrant III vertically upward into Quadrant II across the x-axis.
11 Reflect ΔMNP across line y = 1
Line: y = 1 CORRECT: B
M′ N′ P′
| Vertex |
Pre-Image |
Transformed Image (Solution) |
| M |
(1, 2) |
M′(1, 0) |
| N |
(4, 2) |
N′(4, 0) |
| P |
(1, 4) |
P′(1, −2) |
M and N are 1 unit above y = 1 → reflect to y = 0. P is 3 units above y = 1 → reflects to y = −2.
Module 2: Transformations & Coordinate Geometry Page 3 of 4 • Part III Detailed Solutions
Module 2 • Geometry | Teacher Answer Key
CCSS 8.G.A.3 | Part IV Key (Q12–Q15)
Line Detection & Analysis — Answer Key
Part IV: Transforming Polygons across Specific Lines & Identifying Reflection Line Equations
Part IV Quick Keys:
Q12: C Q13: D Q14: B Q15: A
12 Reflect ΔJKL across line x = 1
CORRECT: C
J′ K′ L′
J(2, 1) is 1 right → J′(0, 1)
K(4, 1) is 3 right → K′(−2, 1)
L(2, 4) is 1 right → L′(0, 4)
13 Detect Line: Fig 1 → Fig 2
CORRECT: D
y = 0 Fig 1 Fig 2
Corresponding y-coordinates are opposites (1 ↔ −1).
The line of symmetry is halfway: (1 + (−1))/2 = 0.
Line: The x-axis (y = 0)
14 Reflect ΔPQR across line y = −1
CORRECT: B
P′ Q′ R′
P, Q are 2 units above y = −1 → reflect 2 below: y = −3.
R is 4 units above y = −1 → reflects 4 below: y = −5.
P′(1, −3), Q′(4, −3), R′(1, −5)
15 Detect Line: Fig 1 → Fig 2
CORRECT: A
x = 0 Fig 1 Fig 2
Vertical legs are at x = −1 and x = 1.
The line of symmetry is halfway: (−1 + 1)/2 = 0.
Line: The y-axis (x = 0)
Pedagogical Tip: Have students sketch the segment connecting corresponding vertices; the perpendicular bisector always defines the reflection line.
Module 2: Transformations & Coordinate Geometry Page 4 of 4 • Part IV Detailed Solutions
