Geometry: Symmetry, Coordinates and Translation
Geometry: Symmetry, Coordinates and Translation is the Year 4 topic covering reflective symmetry, completing a symmetric figure by reflecting its missing half, describing a point's position on a grid as coordinates (x, y), and translating a shape by sliding it without turning or flipping it.
Before you start
Make sure you're comfortable with these topics first:
Method
- To check or complete a line of symmetry, imagine folding the shape along the mirror line: both halves must match exactly, point for point.
- To complete a symmetric figure on a grid, count how many squares each point on the drawn half is from the mirror line, then mark the matching point the same number of squares on the other side, and join the new points up.
- To read a coordinate, always give the along number (x, horizontal) first and the up number (y, vertical) second: think 'along the corridor, then up the stairs'.
- To plot a coordinate (x, y), start at the origin (0, 0), count x squares to the right, then count y squares up, and mark the point there.
- A translation slides every point of a shape the same number of units left or right and the same number of units up or down, so the shape's size, angles and orientation never change.
- To translate a point, add a rightward move to its x-coordinate (subtract for a leftward move) and add an upward move to its y-coordinate (subtract for a downward move).
Worked example
Triangle A has vertices at (1, 1), (1, 4) and (3, 1). Translate triangle A 3 units right and 2 units up to give triangle B. Write the coordinates of triangle B's vertices.
- A translation of 3 right and 2 up means adding 3 to every x-coordinate and adding 2 to every y-coordinate.
- (1, 1) becomes (1 + 3, 1 + 2) = (4, 3).
- (1, 4) becomes (1 + 3, 4 + 2) = (4, 6).
- (3, 1) becomes (3 + 3, 1 + 2) = (6, 3).
- Triangle B has vertices at (4, 3), (4, 6) and (6, 3).
Practice questions
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Q1Point A is at (3, 7). It is translated 2 units right and 3 units down. What are the coordinates of its new position?Show answer
Answer: (5, 4), because 3 + 2 = 5 and 7 - 3 = 4
Q2Which of these capital letters has a vertical line of symmetry: F, H or R?Show answer
Answer: H (a vertical line straight down the middle of an H reflects one half onto the other exactly; F and R do not have a line of symmetry)
Q3A treasure marker on a map is 5 squares along and 2 squares up from the corner of the grid. Write this position as a coordinate pair.Show answer
Answer: (5, 2)
Q4A triangle has corners at (1, 1), (4, 1) and (1, 5). What type of angle is at the corner (1, 1)?Show answer
Answer: A right angle, because one side runs horizontally from (1, 1) to (4, 1) and the other runs vertically from (1, 1) to (1, 5), meeting at 90 degrees
Q5Point B is at (4, 2). It is translated 1 unit right and 5 units up. What are its new coordinates?Show answer
Answer: (5, 7), because 4 + 1 = 5 and 2 + 5 = 7
Q6Freya's counter is at (6, 3) on a games board. She moves it 2 units left and 4 units up. What are the coordinates of its new position?Show answer
Answer: (4, 7), because 6 - 2 = 4 and 3 + 4 = 7
Q7Explain why translating a shape does not change its size or shape.Show answer
Answer: A translation only slides a shape to a new position on the grid; it does not rotate, reflect or resize it, so every side length and every angle stays exactly the same.
Q8Shape D has a vertex at (7, 1). After a translation, that vertex moves to (7, 6). Describe the translation in words.Show answer
Answer: It is a translation of 5 units up with no left or right movement, because the x-coordinate stays at 7 while the y-coordinate increases from 1 to 6.
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A quadrilateral has vertices at (2, 2), (2, 5), (6, 5) and (6, 2). It is translated 3 units right and 1 unit down. Give the new coordinates of the vertex that started at (6, 5).
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Look at the capital letters A, B, N and T. Write down the one letter that does NOT have a line of symmetry.
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Point P starts at (3, 8). It is translated 4 units right and 6 units down to point Q. Point Q is then translated 2 units left and 1 unit up to point R. Work out the coordinates of point R. Show your working.
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Free printable worksheet
Want more practice on paper? Download the geometry: symmetry, coordinates and translation 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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