What does it mean?
A reflection matches each point with a point the same perpendicular distance on the opposite side of a mirror line. It reverses orientation while keeping side lengths and angles unchanged. The distance is measured straight to the line, not diagonally to an arbitrary point on it.
For each point, count the shortest distance to the mirror line. Place the image the same distance on the other side. The reflected shape keeps its size but faces the opposite way.
Learning goal: Reflections. The grade is a suggested starting point; school sequences vary. Use the first worked example to check readiness, and Area and perimeter: the difference, examples and practice if an earlier idea needs revisiting.
See the idea
Read each diagram with its labels, then follow the worked examples. Practice questions include their own measurements and information.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Enlarge diagram to read the labels
Swipe across the enlarged diagram to read every label.
Choose a method and explain why it works
Reflect one vertex at a time. Across a vertical line x = a, keep the y-coordinate and match horizontal distances either side. Across a horizontal line y = b, keep x and match vertical distances. Join the reflected vertices in the same order as the original shape. Points on the mirror line stay where they are.
Notation: same distance from the mirror line
Key rule and when to use it
A reflected point has the same perpendicular distance from the mirror line on the opposite side. A point on the line stays fixed.
Worked examples, step by step
Example 1: Reflect (2, 3) across the vertical line x = 4.
- The point is 2 units left of the line.
- Place the image 2 units right of the line.
- Keep the y-coordinate unchanged.
Answer: (6, 3)
Example 2: Reflect (5, 2) across the horizontal line y = 4.
- The point is 2 units below the line.
- Place the image 2 units above the line.
- Keep the x-coordinate unchanged.
Answer: (5, 6)
Example 3: Reflect point (3, 2) across x = 5, then reflect the image back.
- The point is 2 units left of x = 5, so its image is 2 units right: (7, 2).
- Reflect (7, 2) across the same line: it moves to (3, 2).
- Reflecting twice in the same mirror line returns the original point.
Common mistakes and important boundaries
Sliding a shape across the line without reversing its orientation is a translation, not a reflection. “The same number of squares away” works only if those squares use a consistent scale and the count is perpendicular to the mirror. Do not reflect across an axis when the question names a different line.
A point to explain
A reflection keeps the same perpendicular distance on the other side of the mirror line.
Compare an uncertain attempt with the closest worked example. Look at the meaning of each operation, unit and label before repeating the arithmetic.
Reflection on a Grid and Lines of Symmetry — practice
Work on paper first. Open each answer afterwards and compare the reasoning. Print the questions with or without the separate answer key; no account is required.
Name: ____________________ Date: __________
Point (5, 2) is reflected across the horizontal line y = 4. Where is its image?
Answer and a way to check
(5, 6)
Keep x the same. Match the vertical distance on the other side of y = 4.
Point (1, 4) is reflected across the vertical line x = 3. Where is its image?
Answer and a way to check
(5, 4)
The point is 2 units left of x = 3.
A point lies on the mirror line. Where does its image lie?
Answer and a way to check
At the same point
Its distance from the mirror line is zero.
A triangle is reflected. Which property must stay the same?
Answer and a way to check
Its side lengths
A reflection changes position and orientation but preserves size.
Reflect (4, 1) across x = 4.
Answer and a way to check
(4, 1)
The point lies on the mirror line and therefore has zero distance to move.
Reflect (3, 5) across y = 3.
Answer and a way to check
(3, 1)
It starts 2 units above y = 3, so the image is 2 units below. The x-coordinate stays 3.
Reflect (6, 2) across x = 5.
Answer and a way to check
(4, 2)
The point is one unit right of the mirror; its image is one unit left.
What happens if a shape is reflected twice in the same mirror line?
Answer and a way to check
It returns to its original position.
The second reflection reverses the first point-by-point distance matching.
Reflection on a Grid and Lines of Symmetry — answer key
(5, 6) Keep x the same. Match the vertical distance on the other side of y = 4.
(5, 4) The point is 2 units left of x = 3.
At the same point Its distance from the mirror line is zero.
Its side lengths A reflection changes position and orientation but preserves size.
(4, 1) The point lies on the mirror line and therefore has zero distance to move.
(3, 1) It starts 2 units above y = 3, so the image is 2 units below. The x-coordinate stays 3.
(4, 2) The point is one unit right of the mirror; its image is one unit left.
It returns to its original position. The second reflection reverses the first point-by-point distance matching.
Questions students and parents ask
What is a line of symmetry?
It is a mirror line that maps the complete shape onto itself. A reflection in some other line still creates a reflected image, but that line is not necessarily a symmetry line of the original shape.
Does a reflection change a shape’s area?
No. A reflection preserves lengths and angles, so the reflected shape has the same area and perimeter as the original.
Is this a complete set of textbook exercise solutions?
No. This guide adapts BananaLearn’s own teaching examples and practice. It is not official NCERT material or a promise of the exact chapter sequence in a particular board, country or textbook edition.
What if the examples are still difficult?
Revisit Area and perimeter: the difference, examples and practice. Try the first example with its model, then attempt one fresh question independently. A correct copied answer is not evidence that the method can be used without support.
Help at home
Choose one corner and check its shortest distance to the line on both sides. This is a stronger check than deciding whether the outline looks mirrored.
Keep one example of the learner’s own working. A repeated difficulty across fresh questions can guide a discussion with their teacher; one short practice sheet does not establish a diagnosis or a full mastery profile.
Connect this idea to the next skill
About this guide
Based on BananaLearn’s Grade 5 course lesson “Reflections”. The explanations have been adapted for independent reading; course diagrams are reused where they fit the idea, and missing classroom givens are made explicit in questions.
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