lesson
The centre stays fixed
1 · Learn
An enlargement with positive scale factor less than one reduces distances from the centre in the same ratio. Corresponding angles remain equal. Specify the centre as well as the scale factor to define the transformation.
Area changes by the square of the length factor. A half-size enlargement does not halve the area; it quarters it.
2 · Worked example
With centre (0,0) and scale factor 1/2, point (6,4) maps to (3,2).
3 · Your turn
Enlarge point (8,-2) by factor 1/2 about the origin.
Check your answer
(4,-1).
4 · Apply your learning
Draw the line from the centre through each point and check the distance ratio.
Adult guidance and safety
Check prerequisites, units and reasoning. Provide accurate diagrams and varied practice. Extension content needs suitable prior understanding; no GCSE board, tier or examination readiness is implied by this proposed sequence.
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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.
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.
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