lesson
Describe the whole transformation
1 · Learn
A translation needs a displacement, a reflection needs a mirror line and a rotation needs a centre, angle and direction. These transformations preserve lengths and angles. An enlargement changes lengths according to its scale factor.
A picture of the result alone may not specify a unique transformation. Describe all required information and check several corresponding points, not just one.
2 · Worked example
Reflecting (3,-2) across the y-axis gives (-3,-2). Translating the original by 2 left and 5 up instead gives (1,3).
3 · Your turn
Reflect (-4,3) across the x-axis, then translate the reflected point 6 right and 1 down.
Check your answer
The reflection is (-4,-3); the final point is (2,-4).
4 · Apply your learning
Use triangle A(1,1), B(3,1), C(1,2). Reflect the whole triangle in the x-axis, then translate that image 2 right and 3 up. Give every final vertex and verify the length of the image of AB, not just the position of A.
Adult guidance and safety
Require a reasoned method and an independent check. Use accurate number lines, geometric drawings and data displays where the task needs them. These text models require varied practice and diagnostic assessment before curriculum approval.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
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.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress