lesson
A vector records a displacement
1 · Learn
A two-dimensional column vector gives horizontal and vertical displacement in a stated coordinate system. Adding vectors combines displacements component by component. A vector is not an absolute position unless an origin has been specified.
Opposite vectors have equal magnitude and opposite direction. Order of successive translations does not affect their final combined displacement.
2 · Worked example
Moving (3,2) then (-1,4) gives total displacement (2,6). From position (5,1), the final position is (7,7).
3 · Your turn
From (2,5), translate by (-3,2). Find the new position.
Check your answer
(-1,7).
4 · Apply your learning
Draw the two-step and single-step routes on a grid and compare their start and finish.
Adult guidance and safety
Require reasoning and a check. Provide accurate graphs, construction instruments and varied practice. Annual KS3 allocation is proposed; do not treat these short models as a complete assessed programme.
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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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