Geometry: Coordinates and Transformations
Geometry: Coordinates and Transformations is the Year 6 topic covering plotting and reading coordinates in all four quadrants, where the x and y values can be negative, and transforming shapes by translating them (sliding without changing size or shape) or reflecting them in a given mirror line.
Before you start
Make sure you're comfortable with these topics first:
Method
- Remember a coordinate is always written as (x, y): the x-coordinate, how far across, always comes first, then the y-coordinate, how far up or down, second.
- On a full four-quadrant grid, the x-axis and y-axis cross at the origin, (0, 0); points to the left of the y-axis or below the x-axis have negative coordinates.
- To plot a point, start at the origin, move along the x-axis by the x-coordinate, right if positive and left if negative, then move parallel to the y-axis by the y-coordinate, up if positive and down if negative.
- To translate a shape, move every vertex by the same amount in the same direction; a translation is described by how many squares to move right or left, and how many squares up or down.
- To reflect a shape in a mirror line, such as the x-axis, the y-axis, or another vertical or horizontal line, reflect each vertex separately: count its distance from the mirror line, then plot the same distance on the opposite side.
- A translation changes a shape's position but never its size, orientation or the direction it faces; a reflection changes a shape's position and flips it, like a mirror image.
- After transforming a shape, check the new coordinates by counting squares on the grid rather than only calculating, since it is easy to make a sign error with negative coordinates.
Worked example
Triangle A has vertices at (1, 2), (1, 5) and (3, 2). Triangle A is translated 4 squares left and 3 squares down to give triangle B. Write the coordinates of triangle B.
- Translating 4 squares left means subtracting 4 from every x-coordinate; translating 3 squares down means subtracting 3 from every y-coordinate.
- (1, 2) becomes (1 - 4, 2 - 3) = (-3, -1).
- (1, 5) becomes (1 - 4, 5 - 3) = (-3, 2).
- (3, 2) becomes (3 - 4, 2 - 3) = (-1, -1).
- Triangle B has vertices at (-3, -1), (-3, 2) and (-1, -1).
Practice questions
Try each question, then tap to reveal the answer.
Q1Write the coordinates of the point that is 5 squares to the right of the origin and 3 squares up.Show answer
Answer: (5, 3)
Q2A point is at (-2, 4). It is reflected in the y-axis. What are the coordinates of the reflected point?Show answer
Answer: (2, 4)
Q3A point is at (3, -6). It is reflected in the x-axis. What are the coordinates of the reflected point?Show answer
Answer: (3, 6)
Q4A shape is translated 3 squares right and 2 squares up. A vertex starts at (-4, -1). What are the coordinates of the vertex after the translation?Show answer
Answer: (-1, 1)
Q5A rectangle has three vertices at (-3, 1), (2, 1) and (2, 4). What are the coordinates of the fourth vertex?Show answer
Answer: (-3, 4)
Q6A shape is reflected in the y-axis, then the image is reflected in the x-axis. A vertex starts at (4, 5). What are its coordinates after both reflections?Show answer
Answer: (-4, -5)
Q7Describe the translation that moves the point (-5, 2) to the point (1, -3).Show answer
Answer: 6 squares right and 5 squares down
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
Triangle A has vertices at (-4, 1), (-4, 4) and (-1, 1). Triangle A is reflected in the y-axis to give triangle B. Write the coordinates of the three vertices of triangle B.
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A point at (6, -2) is translated to (2, 3). Describe the translation using the number of squares moved left or right and up or down.
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A square has vertices at (-2, -2), (-2, 2), (2, 2) and (2, -2). Zara says that reflecting this square in the x-axis gives exactly the same square, in exactly the same position. Is Zara correct? Explain your answer using coordinates.
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Free printable worksheet
Want more practice on paper? Download the geometry: coordinates and transformations worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
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