Geometry
Coordinates, Translation and Reflection
Year 3 · Year 4 · Year 5 · Year 6
- ✓By the end of this lesson students will be able to accurately read and plot coordinates in the first quadrant.
- ✓By the end of this lesson students will be able to accurately read and plot coordinates in all four quadrants (Year 6).
- ✓By the end of this lesson students will be able to translate 2-D shapes on a coordinate grid.
- ✓By the end of this lesson students will be able to reflect 2-D shapes across the x-axis or y-axis.
- ✓By the end of this lesson students will be able to describe the translation or reflection of a shape.
Key concepts
A pair of numbers, written as (x, y), that show the exact position of a point on a grid. The first number (x) tells you how far to move horizontally (left or right) from the origin. The second number (y) tells you how far to move vertically (up or down).
The horizontal line on a coordinate grid is called the x-axis. The vertical line is called the y-axis. They meet at the origin.
The point (0, 0) where the x-axis and y-axis cross. It is the starting point for plotting coordinates.
The top-right section of the coordinate grid where both the x and y coordinates are positive numbers. This is usually the first quadrant students learn about.
When the x-axis and y-axis extend to include negative numbers, they divide the grid into four sections called quadrants. Quadrants are numbered anti-clockwise starting from the top-right. Quadrant 1: x is positive, y is positive (top-right) Quadrant 2: x is negative, y is positive (top-left) Quadrant 3: x is negative, y is negative (bottom-left) Quadrant 4: x is positive, y is negative (bottom-right)
Moving a shape from one position to another without turning it, flipping it, or changing its size. It is a 'slide'. Every point in the shape moves the same distance in the same direction. We describe a translation by saying how many units left/right and how many units up/down.
Flipping a shape over a line, called the mirror line. The reflected shape is a mirror image of the original. Each point in the reflected shape is the same distance from the mirror line as the corresponding point in the original shape. For Key Stage 2, mirror lines are usually the x-axis or y-axis.
Key facts to remember
- 1Coordinates are always written as (x, y), where x is the horizontal position and y is the vertical position.
- 2The x-axis is horizontal, and the y-axis is vertical.
- 3The origin is the point (0, 0) where the axes cross.
- 4The first quadrant has positive x and positive y coordinates.
- 5Translation is a 'slide' – the shape moves without turning or changing size.
- 6Reflection is a 'flip' over a mirror line – the shape creates a mirror image.
- 7When reflecting across the x-axis, the x-coordinate stays the same, and the y-coordinate changes sign.
- 8When reflecting across the y-axis, the y-coordinate stays the same, and the x-coordinate changes sign.
Worked examples
Example 1
Plot the points A(2, 1), B(5, 1), and C(3, 4) on a coordinate grid. Join the points to form a triangle.
Answer
A triangle with vertices at (2,1), (5,1), and (3,4).
Always move along the x-axis first, then up the y-axis. Remember 'along the corridor and up the stairs'.
Example 2
Translate triangle ABC with vertices A(1, 2), B(4, 2), C(2, 5) by 3 units right and 1 unit down. Draw the translated triangle A'B'C'.
Answer
Triangle A'B'C' with vertices at (4,1), (7,1), and (5,4).
Each vertex of the shape must be translated by the same amount and in the same direction.
Example 3
Reflect the triangle with vertices P(2, 1), Q(5, 1), R(3, 3) across the x-axis. Draw the reflected triangle P'Q'R'.
Answer
Triangle P'Q'R' with vertices at (2,-1), (5,-1), and (3,-3).
Each point in the reflected shape must be the same perpendicular distance from the mirror line as the original point.
Common mistakes
- ✗Mixing up the x and y coordinates (e.g., plotting (3, 2) instead of (2, 3)).
- ✗Counting the starting square when translating, leading to incorrect distances.
- ✗Forgetting to apply the translation or reflection to all the vertices of a shape.
- ✗Incorrectly calculating negative coordinates, especially when reflecting into different quadrants.
- ✗Drawing a rotation (turn) instead of a translation (slide) or reflection (flip).
Exam tips
- ★Always remember 'along the corridor and up the stairs' for plotting coordinates (x then y).
- ★Use a ruler and a sharp pencil to draw clear axes and shapes.
- ★Label your axes (x and y) and the origin (0) clearly.
- ★When translating, count the number of units carefully for each vertex. Double-check your counting.
- ★When reflecting, check that each new point is the same perpendicular distance from the mirror line as the original point.
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