Lesson 15.2: Reflections, Mirror Images, and Symmetrical Patterns
Applied concepts and practical problem solving for Reflections, Mirror Images, and Symmetrical Patterns.
⏱️ Reading Time: 20 mins
• ❓ 50 Interactive Practice Questions
🌟
Real-Life Story: Symmetry and Symmetrical Designs
Textile Fabric Printing: Printing repeating symmetrical damask and paisley fabric patterns.
💡 Core Mathematical Concepts: Reflections, Mirror Images, and Symmetrical Patterns
Focus areas: Completing shapes across mirror lines and coordinates..
| Concept / Term | Mathematical Meaning | Real-Life Application |
|---|---|---|
| Reflection Transformation | Flipping an object across a mirror line so every point is equidistant on the other side | Mirror image |
| Orientation Inversion | Left and right reverse across a vertical mirror line | Reflection symmetry |
| Symmetrical Grid Completion | Counting squares from mirror line to plot reflection points | Symmetrical drawings |
📝 Step-by-Step Worked Examples
Worked Example 1: Reflect a point 4 units left of mirror
Its reflected image is exactly 4 units right of the mirror line.
Worked Example 2: Letters with symmetry
A, M, T have vertical symmetry; B, C, D, E have horizontal symmetry; H, I, O, X have both!
⚠️ Common Misconceptions to Avoid
Common Misconception: Translating instead of reflecting
Correction: Reflection flips the orientation; sliding without flipping is a translation, not a reflection.
Common Misconception: Measuring distance diagonally to mirror line
Correction: Distance to the mirror line must be measured perpendicular to the line.
🎯
Self-Check Challenge
Which of the following capital letters has BOTH a horizontal line of symmetry and a vertical line of symmetry: A, B, H, or R?
Answer & Explanation:
The letter H has both a horizontal line of symmetry (folding top to bottom) and a vertical line of symmetry (folding left to right).
🎯 Key Learning Takeaways
Extend understanding of Reflections, Mirror Images, and Symmetrical Patterns.
Solve multi-step real-world problems systematically.
Verify solutions through mathematical reasoning.
📄 Printable Worksheets (5 Available)
Download ready-to-print PDFs for offline student practice with separate parent/teacher answer keys.
G5-M-CH15-WS05
A4 • 15 Qs
Symmetry and Symmetrical Designs: Worksheet 5
Practice Assessment 5 • Central Botanical Gardens Context
G5-M-CH15-WS04
A4 • 15 Qs
Symmetry and Symmetrical Designs: Worksheet 4
Practice Assessment 4 • Eco-Friendly Solar Park Context
G5-M-CH15-WS03
A4 • 15 Qs
Symmetry and Symmetrical Designs: Worksheet 3
Practice Assessment 3 • Harbor Marine Terminal Context
G5-M-CH15-WS02
A4 • 15 Qs
Symmetry and Symmetrical Designs: Worksheet 2
Practice Assessment 2 • Science & Discovery Museum Context
G5-M-CH15-WS01
A4 • 15 Qs
Symmetry and Symmetrical Designs: Worksheet 1
Practice Assessment 1 • City Regional Airport Context
✍️ Lesson Practice Questions (50 Questions)
Solve these real-world challenges online, test your understanding, and reveal instant step-by-step explanations.
1
Short Answer
Hard
2 Marks
A symmetrical flag design has a vertical mirror line. If the left side contains 3 blue stars, 2 red stripes, and 1 yellow circle centered on the mirror line, what is the total number of stars and stripes on the full flag?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 stars and 4 stripes
Step-by-Step Explanation:
Left: 3 stars + 2 stripes. Right (reflected): 3 stars + 2 stripes. Total = 6 stars and 4 stripes (the circle sits on the line so remains 1).
2
Short Answer
Hard
2 Marks
Point A has coordinates (3, 5). If Point A is reflected across the vertical mirror line x = 6, what are the coordinates of the reflected point A'?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(9, 5)
Step-by-Step Explanation:
Distance from x=3 to line x=6 is 3 units. Moving 3 units past x=6 gives 6 + 3 = 9. The coordinates are (9, 5).
3
Short Answer
Hard
2 Marks
Why does a circle have infinitely many lines of symmetry while a regular polygon has a finite number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A circle consists of all points equidistant from a single center point. Any diameter drawn at any angle through the center bisects the circle into identical halves.
Step-by-Step Explanation:
Rotational invariance at all continuous angles yields infinite diameter symmetry axes.
4
Short Answer
Hard
2 Marks
Explain why an object and its reflected mirror image are congruent even though their orientations are reversed.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection preserves all side lengths, perimeter, area, and internal angles unchanged. Because all geometric dimensions match exactly, the shapes are congruent, despite being chiral (mirror) opposites.
Step-by-Step Explanation:
Isometries preserve distances and angles, ensuring full geometric congruence.
5
Short Answer
Medium
1 Mark
A student claims that the letter 'N' has a line of symmetry down the middle diagonal. Why is this incorrect?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflecting across the diagonal does not map the vertical stems onto each other (N has rotational, not reflective symmetry)
Step-by-Step Explanation:
Flipping 'N' across its diagonal inverts the orientations; it has rotational symmetry of 180°, not mirror symmetry.
6
Short Answer
Medium
1 Mark
Chris says: 'Every rectangle has 4 lines of symmetry just like a square.' Identify Chris's error and state the correct number of symmetry lines for a non-square rectangle.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 lines of symmetry
Step-by-Step Explanation:
A standard rectangle's diagonals do not form lines of symmetry. It only has 2 lines of symmetry connecting opposite side midpoints.
7
Fill in the Blanks
Medium
1 Mark
Identify the shape: A circle has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
infinite
Step-by-Step Explanation:
Any straight line passing through the center of a circle is a line of symmetry, giving infinite lines.
8
Fill in the Blanks
Medium
1 Mark
Complete the geometric symmetry rule: A regular pentagon has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
A regular 5-sided pentagon has 5 lines of symmetry.
9
Short Answer
Medium
1 Mark
Which of these capital letters has zero lines of symmetry: M, T, S, or Y?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
S
Step-by-Step Explanation:
The letter 'S' has rotational symmetry of order 2, but 0 lines of reflective symmetry.
10
Short Answer
Medium
1 Mark
A butterfly design is drawn with its center on a vertical mirror line. If the left wing tip is 14 cm from the mirror line, how far from the mirror line is the right wing tip?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 cm
Step-by-Step Explanation:
Line symmetry maintains equal perpendicular distances from the mirror line.
11
Short Answer
Medium
1 Mark
At the Central Botanical Gardens, an artisan creates mosaic tiles. A regular hexagon tile is placed on the floor. How many different lines of symmetry can be drawn across this regular hexagon?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 lines
Step-by-Step Explanation:
A regular polygon with n sides has n lines of symmetry. A regular hexagon has 6 lines of symmetry.
12
Multiple Choice
Easy
1 Mark
What type of transformation creates a mirror image across a line of symmetry?
A
Reflection
B
Rotation
C
Translation
D
Enlargement
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection
Step-by-Step Explanation:
Reflection flips a figure across a mirror line to produce a symmetrical image.
13
Multiple Choice
Easy
1 Mark
How many lines of symmetry does an equilateral triangle possess?
A
3 lines
B
1 line
C
2 lines
D
0 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 lines
Step-by-Step Explanation:
An equilateral triangle has 3 lines of symmetry from each vertex to the midpoint of the opposite side.
14
Multiple Choice
Easy
1 Mark
Which of the following capital letters has both a horizontal and a vertical line of symmetry?
A
H
B
A
C
B
D
F
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
H
Step-by-Step Explanation:
The letter 'H' can be folded horizontally and vertically into identical matching halves.
15
Multiple Choice
Easy
1 Mark
How many lines of symmetry does a regular square have?
A
4 lines
B
2 lines
C
1 line
D
8 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 lines
Step-by-Step Explanation:
A square has 4 lines of symmetry: 2 through opposite side midpoints and 2 along diagonals.
16
Short Answer
Hard
2 Marks
A symmetrical flag design has a vertical mirror line. If the left side contains 3 blue stars, 2 red stripes, and 1 yellow circle centered on the mirror line, what is the total number of stars and stripes on the full flag?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 stars and 4 stripes
Step-by-Step Explanation:
Left: 3 stars + 2 stripes. Right (reflected): 3 stars + 2 stripes. Total = 6 stars and 4 stripes (the circle sits on the line so remains 1).
17
Short Answer
Hard
2 Marks
Point A has coordinates (3, 5). If Point A is reflected across the vertical mirror line x = 6, what are the coordinates of the reflected point A'?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(9, 5)
Step-by-Step Explanation:
Distance from x=3 to line x=6 is 3 units. Moving 3 units past x=6 gives 6 + 3 = 9. The coordinates are (9, 5).
18
Short Answer
Hard
2 Marks
Why does a circle have infinitely many lines of symmetry while a regular polygon has a finite number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A circle consists of all points equidistant from a single center point. Any diameter drawn at any angle through the center bisects the circle into identical halves.
Step-by-Step Explanation:
Rotational invariance at all continuous angles yields infinite diameter symmetry axes.
19
Short Answer
Hard
2 Marks
Explain why an object and its reflected mirror image are congruent even though their orientations are reversed.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection preserves all side lengths, perimeter, area, and internal angles unchanged. Because all geometric dimensions match exactly, the shapes are congruent, despite being chiral (mirror) opposites.
Step-by-Step Explanation:
Isometries preserve distances and angles, ensuring full geometric congruence.
20
Short Answer
Medium
1 Mark
A student claims that the letter 'N' has a line of symmetry down the middle diagonal. Why is this incorrect?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflecting across the diagonal does not map the vertical stems onto each other (N has rotational, not reflective symmetry)
Step-by-Step Explanation:
Flipping 'N' across its diagonal inverts the orientations; it has rotational symmetry of 180°, not mirror symmetry.
21
Short Answer
Medium
1 Mark
Chris says: 'Every rectangle has 4 lines of symmetry just like a square.' Identify Chris's error and state the correct number of symmetry lines for a non-square rectangle.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 lines of symmetry
Step-by-Step Explanation:
A standard rectangle's diagonals do not form lines of symmetry. It only has 2 lines of symmetry connecting opposite side midpoints.
22
Fill in the Blanks
Medium
1 Mark
Identify the shape: A circle has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
infinite
Step-by-Step Explanation:
Any straight line passing through the center of a circle is a line of symmetry, giving infinite lines.
23
Fill in the Blanks
Medium
1 Mark
Complete the geometric symmetry rule: A regular pentagon has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
A regular 5-sided pentagon has 5 lines of symmetry.
24
Short Answer
Medium
1 Mark
Which of these capital letters has zero lines of symmetry: M, T, S, or Y?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
S
Step-by-Step Explanation:
The letter 'S' has rotational symmetry of order 2, but 0 lines of reflective symmetry.
25
Short Answer
Medium
1 Mark
A butterfly design is drawn with its center on a vertical mirror line. If the left wing tip is 14 cm from the mirror line, how far from the mirror line is the right wing tip?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 cm
Step-by-Step Explanation:
Line symmetry maintains equal perpendicular distances from the mirror line.
26
Short Answer
Medium
1 Mark
At the Eco-Friendly Solar Park, an artisan creates mosaic tiles. A regular hexagon tile is placed on the floor. How many different lines of symmetry can be drawn across this regular hexagon?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 lines
Step-by-Step Explanation:
A regular polygon with n sides has n lines of symmetry. A regular hexagon has 6 lines of symmetry.
27
Multiple Choice
Easy
1 Mark
What type of transformation creates a mirror image across a line of symmetry?
A
Reflection
B
Rotation
C
Translation
D
Enlargement
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection
Step-by-Step Explanation:
Reflection flips a figure across a mirror line to produce a symmetrical image.
28
Multiple Choice
Easy
1 Mark
How many lines of symmetry does an equilateral triangle possess?
A
3 lines
B
1 line
C
2 lines
D
0 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 lines
Step-by-Step Explanation:
An equilateral triangle has 3 lines of symmetry from each vertex to the midpoint of the opposite side.
29
Multiple Choice
Easy
1 Mark
Which of the following capital letters has both a horizontal and a vertical line of symmetry?
A
H
B
A
C
B
D
F
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
H
Step-by-Step Explanation:
The letter 'H' can be folded horizontally and vertically into identical matching halves.
30
Multiple Choice
Easy
1 Mark
How many lines of symmetry does a regular square have?
A
4 lines
B
2 lines
C
1 line
D
8 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 lines
Step-by-Step Explanation:
A square has 4 lines of symmetry: 2 through opposite side midpoints and 2 along diagonals.
31
Short Answer
Hard
2 Marks
A symmetrical flag design has a vertical mirror line. If the left side contains 3 blue stars, 2 red stripes, and 1 yellow circle centered on the mirror line, what is the total number of stars and stripes on the full flag?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 stars and 4 stripes
Step-by-Step Explanation:
Left: 3 stars + 2 stripes. Right (reflected): 3 stars + 2 stripes. Total = 6 stars and 4 stripes (the circle sits on the line so remains 1).
32
Short Answer
Hard
2 Marks
Point A has coordinates (3, 5). If Point A is reflected across the vertical mirror line x = 6, what are the coordinates of the reflected point A'?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(9, 5)
Step-by-Step Explanation:
Distance from x=3 to line x=6 is 3 units. Moving 3 units past x=6 gives 6 + 3 = 9. The coordinates are (9, 5).
33
Short Answer
Hard
2 Marks
Why does a circle have infinitely many lines of symmetry while a regular polygon has a finite number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A circle consists of all points equidistant from a single center point. Any diameter drawn at any angle through the center bisects the circle into identical halves.
Step-by-Step Explanation:
Rotational invariance at all continuous angles yields infinite diameter symmetry axes.
34
Short Answer
Hard
2 Marks
Explain why an object and its reflected mirror image are congruent even though their orientations are reversed.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection preserves all side lengths, perimeter, area, and internal angles unchanged. Because all geometric dimensions match exactly, the shapes are congruent, despite being chiral (mirror) opposites.
Step-by-Step Explanation:
Isometries preserve distances and angles, ensuring full geometric congruence.
35
Short Answer
Medium
1 Mark
A student claims that the letter 'N' has a line of symmetry down the middle diagonal. Why is this incorrect?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflecting across the diagonal does not map the vertical stems onto each other (N has rotational, not reflective symmetry)
Step-by-Step Explanation:
Flipping 'N' across its diagonal inverts the orientations; it has rotational symmetry of 180°, not mirror symmetry.
36
Short Answer
Medium
1 Mark
Chris says: 'Every rectangle has 4 lines of symmetry just like a square.' Identify Chris's error and state the correct number of symmetry lines for a non-square rectangle.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
2 lines of symmetry
Step-by-Step Explanation:
A standard rectangle's diagonals do not form lines of symmetry. It only has 2 lines of symmetry connecting opposite side midpoints.
37
Fill in the Blanks
Medium
1 Mark
Identify the shape: A circle has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
infinite
Step-by-Step Explanation:
Any straight line passing through the center of a circle is a line of symmetry, giving infinite lines.
38
Fill in the Blanks
Medium
1 Mark
Complete the geometric symmetry rule: A regular pentagon has [ ? ] lines of symmetry.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
5
Step-by-Step Explanation:
A regular 5-sided pentagon has 5 lines of symmetry.
39
Short Answer
Medium
1 Mark
Which of these capital letters has zero lines of symmetry: M, T, S, or Y?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
S
Step-by-Step Explanation:
The letter 'S' has rotational symmetry of order 2, but 0 lines of reflective symmetry.
40
Short Answer
Medium
1 Mark
A butterfly design is drawn with its center on a vertical mirror line. If the left wing tip is 14 cm from the mirror line, how far from the mirror line is the right wing tip?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
14 cm
Step-by-Step Explanation:
Line symmetry maintains equal perpendicular distances from the mirror line.
41
Short Answer
Medium
1 Mark
At the Harbor Marine Terminal, an artisan creates mosaic tiles. A regular hexagon tile is placed on the floor. How many different lines of symmetry can be drawn across this regular hexagon?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 lines
Step-by-Step Explanation:
A regular polygon with n sides has n lines of symmetry. A regular hexagon has 6 lines of symmetry.
42
Multiple Choice
Easy
1 Mark
What type of transformation creates a mirror image across a line of symmetry?
A
Reflection
B
Rotation
C
Translation
D
Enlargement
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection
Step-by-Step Explanation:
Reflection flips a figure across a mirror line to produce a symmetrical image.
43
Multiple Choice
Easy
1 Mark
How many lines of symmetry does an equilateral triangle possess?
A
3 lines
B
1 line
C
2 lines
D
0 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
3 lines
Step-by-Step Explanation:
An equilateral triangle has 3 lines of symmetry from each vertex to the midpoint of the opposite side.
44
Multiple Choice
Easy
1 Mark
Which of the following capital letters has both a horizontal and a vertical line of symmetry?
A
H
B
A
C
B
D
F
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
H
Step-by-Step Explanation:
The letter 'H' can be folded horizontally and vertically into identical matching halves.
45
Multiple Choice
Easy
1 Mark
How many lines of symmetry does a regular square have?
A
4 lines
B
2 lines
C
1 line
D
8 lines
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
4 lines
Step-by-Step Explanation:
A square has 4 lines of symmetry: 2 through opposite side midpoints and 2 along diagonals.
46
Short Answer
Hard
2 Marks
A symmetrical flag design has a vertical mirror line. If the left side contains 3 blue stars, 2 red stripes, and 1 yellow circle centered on the mirror line, what is the total number of stars and stripes on the full flag?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
6 stars and 4 stripes
Step-by-Step Explanation:
Left: 3 stars + 2 stripes. Right (reflected): 3 stars + 2 stripes. Total = 6 stars and 4 stripes (the circle sits on the line so remains 1).
47
Short Answer
Hard
2 Marks
Point A has coordinates (3, 5). If Point A is reflected across the vertical mirror line x = 6, what are the coordinates of the reflected point A'?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
(9, 5)
Step-by-Step Explanation:
Distance from x=3 to line x=6 is 3 units. Moving 3 units past x=6 gives 6 + 3 = 9. The coordinates are (9, 5).
48
Short Answer
Hard
2 Marks
Why does a circle have infinitely many lines of symmetry while a regular polygon has a finite number?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
A circle consists of all points equidistant from a single center point. Any diameter drawn at any angle through the center bisects the circle into identical halves.
Step-by-Step Explanation:
Rotational invariance at all continuous angles yields infinite diameter symmetry axes.
49
Short Answer
Hard
2 Marks
Explain why an object and its reflected mirror image are congruent even though their orientations are reversed.
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflection preserves all side lengths, perimeter, area, and internal angles unchanged. Because all geometric dimensions match exactly, the shapes are congruent, despite being chiral (mirror) opposites.
Step-by-Step Explanation:
Isometries preserve distances and angles, ensuring full geometric congruence.
50
Short Answer
Medium
1 Mark
A student claims that the letter 'N' has a line of symmetry down the middle diagonal. Why is this incorrect?
💡 Click to View Correct Answer & Explanation ▼
Correct Answer:
Reflecting across the diagonal does not map the vertical stems onto each other (N has rotational, not reflective symmetry)
Step-by-Step Explanation:
Flipping 'N' across its diagonal inverts the orientations; it has rotational symmetry of 180°, not mirror symmetry.