Symmetrical Figures and Patterns
Semester 4B · Chapter 16 · Lesson 6 · MATH-4B-C16-L06
Before you begin: prerequisite check
Recall: 16.05. Attempt these questions independently first.
A folded shape has the shape of a square. How many reflection-symmetry lines does it have?
Show answer and reasoning
Square figures have 4 exact fold axes.
A chalkboard diagram has the shape of an isosceles non-equilateral triangle. How many reflection-symmetry lines does it have?
Show answer and reasoning
Isosceles non-equilateral triangle figures have 1 exact fold axes.
A paper cutout has the shape of an equilateral triangle. How many reflection-symmetry lines does it have?
Show answer and reasoning
Equilateral triangle figures have 3 exact fold axes.
Key vocabulary
- perpendicular
- meeting at a right angle
- parallel
- same direction and no intersection in a plane
- quadrilateral
- four-sided polygon
- line of symmetry
- line reflecting one matching half onto the other
Understand the concept
To complete a reflected pattern on a grid, mark the distance from each known point to the mirror line, then place its reflection the same distance on the opposite side. Reflect all vertices and join them in the same order. For a vertical mirror line, the left-right position reverses while the vertical level stays the same. For a horizontal mirror line, the up-down position reverses. Points exactly on the mirror line remain fixed, so they should not be duplicated.
Fully worked examples and immediate checks
Read each example, predict how to begin, then follow its numerical explanation. The check below it is a fresh problem.
Worked example 1
Reflect vertices (2,1), (5,3), and (4,6) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Check 1: try it yourself
Reflect vertices (2,1), (5,3), and (3,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Worked example 2
Reflect vertices (1,2), (5,2), and (3,6) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Check 2: try it yourself
Reflect vertices (2,2), (5,3), and (4,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Worked example 3
Reflect vertices (1,2), (4,2), and (3,7) across x = 6. Give reflected points and draw the image.
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Check 3: try it yourself
Reflect vertices (1,1), (4,2), and (3,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Guided practice
Reflect vertices (2,1), (5,2), and (2,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,2), (5,3), and (3,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (5,3), and (3,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (5,2), and (2,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (4,3), and (4,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Independent practice
Reflect vertices (1,1), (5,3), and (2,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (4,3), and (4,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (1,2), (5,2), and (2,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (1,1), (5,2), and (2,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (4,3), and (4,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (4,2), and (2,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (1,2), (5,2), and (3,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (2,1), (4,2), and (4,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Challenge and transfer
Use a diagram or verbal justification where appropriate. The goal is transfer rather than speed.
Reflect vertices (1,2), (5,3), and (2,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
A learner claims: “Reflecting a figure across a vertical line is the same as sliding it sideways.” Identify what is wrong or incomplete and give a mathematically correct explanation.
Show answer and reasoning
False: reflected points must lie at equal perpendicular distances on opposite sides, reversing orientation. Explain the relevant quantities or properties, not merely the final answer.
Exit check
Reflect vertices (1,2), (4,2), and (4,5) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (1,2), (4,2), and (2,6) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Reflect vertices (1,2), (4,3), and (3,7) across x = 6. Give reflected points and draw the image.
Show answer and reasoning
For x=6, the reflected horizontal coordinate is 12−x; all y-coordinates remain unchanged.
Mastery check: Solve a new instance without hints, explain why the method works, and return later to confirm retention.