Introduction to Reflection on a Co-ordinate Grid

Hello Year 5! Today, we’re going to learn about a fun concept in Maths called reflection. Reflection is like looking in a mirror. When you stand in front of a mirror, your image shows up on the other side. In Maths, reflection works the same way on a co-ordinate grid!

What is a Co-ordinate Grid?

A co-ordinate grid is a big square made up of horizontal and vertical lines. It has two axes:

  • X-axis (the horizontal line)
  • Y-axis (the vertical line)

Each point on the grid is marked by a pair of numbers called coordinates. The first number tells you how far to go left or right (X), and the second number tells you how far to go up or down (Y). For example, the point (3, 2) means you go 3 steps to the right and 2 steps up.

What is Reflection?

When we reflect a shape on a co-ordinate grid, we flip it over a line. This line is often one of the axes (X or Y-axis) or a vertical or horizontal line. The shape’s new position is called the image.

Key Rules for Reflection

  1. Reflecting over the X-axis:
    • If a point is at (x, y), when we reflect it over the X-axis, the new point will be (x, -y).
    • Example: Reflect (2, 3) over the X-axis to get (2, -3).
  2. Reflecting over the Y-axis:
    • If a point is at (x, y), when we reflect it over the Y-axis, the new point will be (-x, y).
    • Example: Reflect (4, 1) over the Y-axis to get (-4, 1).
  3. Reflecting over the line y = x:
    • If a point is at (x, y), when we reflect it over the line y = x, the new point will be (y, x).
    • Example: Reflect (5, 2) over the line y = x to get (2, 5).

Tips and Tricks

  • Draw It Out: When you reflect a shape, draw it on the grid first and then draw its reflection. It helps you see the transformation.
  • Use a Mirror: Imagine holding a mirror along the line you are reflecting over. The reflected shape should look like its image in the mirror.
  • Practice with Points: Start with simple points before moving to shapes. Understanding points makes it easier to reflect bigger shapes.

Questions on Reflection

Easy Level Questions

  1. Reflect the point (2, 3) over the X-axis.
  2. Reflect the point (1, 4) over the Y-axis.
  3. What is the reflection of (0, 5) over the X-axis?
  4. Reflect (3, -2) over the Y-axis. What do you get?
  5. If you reflect (5, 5) over the line y = x, what do you get?
  6. Reflect the point (2, -3) over the X-axis.
  7. What is the reflection of (4, 0) over the Y-axis?
  8. Reflect (6, 1) over the line y = x.
  9. What is the reflected point of (0, 3) over the X-axis?
  10. If you reflect (3, 2) over the Y-axis, what is the new point?
  11. Reflect the point (1, 1) over the line y = x.
  12. What do you get when you reflect (2, 2) over the X-axis?
  13. Reflect (5, 3) over the Y-axis. What do you find?
  14. What is the reflection of (0, -4) over the X-axis?
  15. Reflect the point (3, 0) over the line y = x.
  16. If you reflect (1, -2) over the X-axis, what do you get?
  17. Reflect (2, 3) over the Y-axis.
  18. What is the reflection of (4, 5) over the line y = x?
  19. Reflect the point (-3, 0) over the X-axis.
  20. What do you get when you reflect (1, 1) over the Y-axis?

Medium Level Questions

  1. Reflect the triangle with vertices at (1, 2), (3, 2), and (2, 4) over the X-axis. What are the new vertices?
  2. What are the coordinates of the reflection of (4, -2) over the Y-axis?
  3. Reflect the rectangle with corners at (1, 1), (1, 3), (4, 1), and (4, 3) over the line y = x. What are the new corners?
  4. If the point (1, 4) is reflected over the Y-axis and then over the X-axis, what are the coordinates?
  5. Reflect the point (-2, 3) over the line y = x. What do you get?
  6. What is the reflection of the point (3, 5) over the line y = x?
  7. If you reflect the point (0, 2) over the X-axis and then the Y-axis, what are the new coordinates?
  8. Reflect the point (2, 2) over the line y = x and then over the X-axis. What is the final point?
  9. Find the reflection of the point (5, 5) first over the Y-axis and then over the X-axis.
  10. Reflect the point (-4, -1) over the X-axis. What do you get?
  11. What are the coordinates of the reflection of (3, 6) over the Y-axis?
  12. If you reflect (2, 3) over the line y = x and then over the Y-axis, what is the new point?
  13. Reflect the square with vertices (1, 1), (1, 4), (4, 1), and (4, 4) over the X-axis. What are the new vertices?
  14. What do you get when you reflect the point (6, -2) over the Y-axis and then over the line y = x?
  15. Reflect the point (2, 5) over the X-axis. What is the new point?
  16. If the point (1, -3) is reflected over the Y-axis, what is the new coordinate?
  17. Find the reflection of the point (-2, 2) over the line y = x.
  18. Reflect the point (0, 3) first over the X-axis and then over the Y-axis. What is the final point?
  19. If you reflect (1, 1) over the line y = x and then reflect that point over the X-axis, what do you get?
  20. Reflect the points of a triangle at (0, 0), (1, 2), and (2, 1) over the Y-axis. What are the new coordinates?

Hard Level Questions

  1. Reflect the quadrilateral with vertices (1, 2), (2, 5), (5, 3), and (4, 1) over the X-axis. What are the new vertices?
  2. If a point (a, b) is reflected over the line y = x, what are the coordinates of the new point in terms of a and b?
  3. Find the reflection of the point (3, -6) over the Y-axis and then over the line y = x. What is the new point?
  4. Reflect the triangle with vertices (2, 3), (4, 1), and (3, 5) over the X-axis. What are the new vertices?
  5. If you reflect the point (1, 6) over the Y-axis and then over the X-axis, what are the new coordinates?
  6. A rectangle has corners at (2, 3), (2, 6), (5, 3), and (5, 6). Reflect it over the line y = x. What are the new corners?
  7. Reflect the point (-3, 4) over the line y = x and then over the X-axis. What do you get?
  8. What is the reflection of the trapezium with vertices (2, 1), (4, 4), (3, 5), and (1, 2) over the Y-axis?
  9. If the point (4, -5) is reflected over the X-axis and then reflected over the line y = x, what are the coordinates?
  10. Reflect the point (2, 2) over the line y = x and then find the distance between the original point and its reflection.
  11. A pentagon has vertices at (1, 2), (3, 4), (4, 2), (2, 0), and (0, 1). Reflect it over the X-axis. What are the new vertices?
  12. What is the new point when the point (a, b) is reflected first over the X-axis and then over the Y-axis?
  13. If you reflect the point (2, -3) over both the X-axis and the Y-axis, what do you find?
  14. Reflect the triangle with vertices at (0, 0), (0, 2), and (2, 0) over the line y = x. What are the new vertices?
  15. If the point (x, y) is reflected over the line y = x and then over the Y-axis, what are the new coordinates in terms of x and y?
  16. Reflect the square with vertices at (1, 1), (1, 3), (3, 1), and (3, 3) over the line y = x. What are the new vertices?
  17. If you reflect the point (5, 5) over the X-axis and then reflect that point over the Y-axis, what do you get?
  18. Reflect the point (-4, -3) over the line y = x and then over the X-axis. What is the final point?
  19. What will the coordinates be if the point (a, b) is reflected first over the Y-axis and then over the line y = x?
  20. Reflect the quadrilateral with vertices (1, 1), (3, 1), (3, 4), and (1, 4) over the X-axis. What are the new vertices?

Answers and Explanations

Easy Level Answers

  1. (2, -3)
  2. (-1, 4)
  3. (0, -5)
  4. (-3, -2)
  5. (5, 1)
  6. (2, 3)
  7. (-4, 0)
  8. (1, 6)
  9. (0, 3)
  10. (-3, 2)
  11. (1, 1)
  12. (2, -2)
  13. (-5, 3)
  14. (0, 4)
  15. (1, -1)
  16. (2, 2)
  17. (-2, 3)
  18. (4, 4)
  19. (-3, 3)
  20. (1, 1)

Medium Level Answers

  1. (1, -2), (3, -2), (2, -4)
  2. (-4, -2)
  3. (1, 1), (1, 3), (4, 1), (4, 3)
  4. (1, -4)
  5. (-3, -2)
  6. (3, 5)
  7. (0, -2)
  8. (-2, 2)
  9. (-6, -4)
  10. (-4, 2)
  11. (3, 1)
  12. (3, 2)
  13. (1, -3)
  14. (1, -1), (3, -1), (4, -1), (1, -4)
  15. (1, -3)
  16. (1, 1), (1, 3), (3, 1), (3, 3)
  17. (-5, -5)
  18. (-4, 3)
  19. (1, a)
  20. (1, -1), (3, -1), (3, -4), (1, -4)

Hard Level Answers

  1. (1, -2), (2, -5), (5, -3), (4, -1)
  2. (b, a)
  3. (3, 6)
  4. (2, -3), (4, -1), (3, -5)
  5. (1, 6)
  6. (2, 2), (2, -6), (5, 2), (5, -6)
  7. (3, 4)
  8. (-2, 1), (-4, -4), (-3, -5), (-1, -2)
  9. (4, 5)
  10. (2, 2) and distance is $$d = \sqrt{(2-2)^2 + (2-2)^2} = 0$$
  11. (1, -2), (3, -4), (4, -2), (2, 0)
  12. (-a, -b)
  13. (-2, 3)
  14. (0, 0), (0, 2), (2, 0)
  15. (-y, x)
  16. (1, 1), (3, 1), (3, 3), (1, 3)
  17. (-5, -5)
  18. (4, 3)
  19. (-a, b)
  20. (1, -1), (3, -1), (3, -4), (1, -4)

I hope this helps you understand reflections on a co-ordinate grid better! Keep practicing, and you’ll get the hang of it in no time!