lesson
Read horizontal position first
1 · Learn
Coordinates (x,y) give horizontal position first and vertical position second. Negative coordinates extend the grid left of and below the origin. Translation moves every point by the same displacement without changing shape or orientation.
Reflection across an axis changes positions according to that mirror line. Across the y-axis, the x sign changes and y stays fixed; across the x-axis, the reverse happens.
2 · Worked example
A point (-3,2) translated 5 right and 4 down becomes (2,-2). Reflected across the y-axis instead, the original becomes (3,2). These are different transformations.
3 · Your turn
Translate (-4,-1) by 6 right and 3 up. Reflect the original point across the x-axis.
Check your answer
The translation gives (2,2). The reflection of the original gives (-4,1).
4 · Apply your learning
Plot a triangle and transform every vertex, checking that side lengths remain unchanged.
Adult guidance and safety
Ask the learner to explain the method and check it using a different representation. Supply place-value grids, fraction strips, accurate diagrams and measuring tools where needed. These examples need varied practice; a short correct answer alone does not establish fluency.
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Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
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