What is Reflection?

Reflection in maths is when we flip a shape over a line. Imagine you have a mirror. When you look in a mirror, you see a reflection of yourself. In geometry, we do something similar with shapes.

Key Terms

  1. Line of Reflection: This is the line that acts like the mirror. It can be horizontal, vertical, or diagonal.
  2. Reflected Image: This is the new shape that appears after the reflection.

How to Reflect a Shape

To reflect a shape, follow these steps:

  1. Identify the Line of Reflection: Decide where your mirror line is. For example, it could be the x-axis (horizontal line) or y-axis (vertical line).
  2. Measure the Distance: From each point of the shape, measure how far it is to the line of reflection.
  3. Mark the New Points: From the line of reflection, measure the same distance on the other side to find the new points.
  4. Connect the Dots: Draw the new shape using the new points you found.

Example

Let’s say we have a triangle with points A(1, 2), B(4, 2), and C(2, 5). If we reflect this triangle over the y-axis:

  1. Identify the Line: The y-axis is our line of reflection.
  2. Measure the Distance:
    • A(1, 2) is 1 unit from the y-axis.
    • B(4, 2) is 4 units from the y-axis.
    • C(2, 5) is 2 units from the y-axis.
  3. Mark the New Points:
    • A’ will be (-1, 2),
    • B’ will be (-4, 2),
    • C’ will be (-2, 5).
  4. Connect the Dots: Draw triangle A’B’C’.

Key Rules

  1. Distance: The distance from the original point to the line of reflection is the same as from the line to the reflected point.
  2. Coordinates Change: If reflecting over the x-axis, the y-coordinate changes sign. If reflecting over the y-axis, the x-coordinate changes sign.
  3. Shapes Stay the Same: The size and shape of the reflected image are exactly the same as the original.

Tips and Tricks

  • Use a ruler to measure distances accurately.
  • Plot the original and reflected points on graph paper to visualize the reflection better.
  • Practice with different shapes and lines of reflection to build confidence.

Questions

Easy Level Questions

  1. What is reflection in maths?
  2. What do we call the line we reflect over?
  3. If point A(2, 3) is reflected over the x-axis, what is the new point?
  4. Reflect the point B(5, 1) over the y-axis.
  5. True or False: The reflected shape is always the same size as the original.
  6. What happens to the y-coordinate when reflecting over the x-axis?
  7. What happens to the x-coordinate when reflecting over the y-axis?
  8. Can a shape be reflected diagonally? Yes or No?
  9. If point C(3, 4) is reflected over the y-axis, what is the reflected point?
  10. Name one shape that you can reflect.

Medium Level Questions

  1. Reflect the triangle with vertices D(1, 3), E(3, 5), F(5, 1) over the x-axis.
  2. If a square has vertices at G(2, 2), H(2, 6), I(6, 6), J(6, 2), what are the new coordinates after reflecting over the y-axis?
  3. How does reflecting a shape change its position?
  4. What is the line of reflection if the shape is flipped vertically?
  5. Reflect point K(-2, 3) over the x-axis. What is the new point?
  6. If point L(4, 2) is reflected over the line y = x, what is the new point?
  7. Draw a shape and reflect it over the y-axis. Describe the process.
  8. If a point is at (0, 5) and is reflected over the x-axis, where does it go?
  9. How do you know if your reflection is correct?
  10. What is the relationship between the original shape and the reflected shape?

Hard Level Questions

  1. Reflect the rectangle with vertices P(2, 3), Q(2, 7), R(6, 7), and S(6, 3) over the line x = 4.
  2. If a triangle has vertices at T(1, 4), U(3, 6), and V(5, 2), what are the new coordinates after reflecting over the line y = 2?
  3. Describe the difference between reflecting over the x-axis and the line y = x.
  4. Create a shape, reflect it over the x-axis, and then reflect the new shape over the y-axis. What do you notice?
  5. If a point M(-3, -4) is reflected over both the x-axis and the y-axis, what is the final position?
  6. If you reflect a star shape over the line y = -1, how would the points change?
  7. Reflect a pentagon with vertices N(1, 1), O(2, 2), P(3, 1), Q(2, 0), R(1, 0) over the y-axis. What are the new coordinates?
  8. If you have a circle centered at (3, 4) and you reflect it over the x-axis, what is the new center?
  9. How does the reflection of a shape help us understand symmetry?
  10. If a shape is reflected over a diagonal line, what additional steps do you need to take?

Answers

Easy Level Answers

  1. Reflection is when we flip a shape over a line.
  2. The line we reflect over is called the line of reflection.
  3. A'(2, -3).
  4. B'(-5, 1).
  5. True.
  6. The y-coordinate changes sign.
  7. The x-coordinate changes sign.
  8. Yes.
  9. C'(-3, 4).
  10. Any shape (e.g., triangle, square).

Medium Level Answers

  1. D'(1, -3), E'(3, -5), F'(5, -1).
  2. G'(−2, 2), H'(−2, 6), I'(−6, 6), J'(−6, 2).
  3. It changes position but not size or shape.
  4. The line would be vertical.
  5. K'(-2, -3).
  6. L'(4, 4).
  7. Draw a shape, measure distances to the line, mark new points, connect the dots.
  8. It goes to (0, -5).
  9. The distances should be equal from the line of reflection.
  10. They are the same shape and size but in different positions.

Hard Level Answers

  1. P'(6, 3), Q'(6, 7), R'(2, 7), S'(2, 3).
  2. T'(1, 0), U'(3, 0), V'(5, 4).
  3. Reflecting over the x-axis changes the y-coordinates, while y = x swaps x and y.
  4. The new shape will be in a different position but still the same shape.
  5. M'(3, 4).
  6. The points would shift downwards and reflect symmetrically.
  7. N'(-1, 1), O'(-2, 2), P'(-3, 1), Q'(-2, 0), R'(-1, 0).
  8. The new center is (3, -4).
  9. It shows us how shapes can be symmetrical.
  10. You need to measure the distance from the points to the line and then measure the same distance on the other side.

Feel free to ask questions or let me know if you need more practice! Happy reflecting!