Reflections, rotations and enlargements · Higher · Réflexions, rotations et agrandissements · Niveau supérieur
| English | Français |
|---|---|
| centre of enlargement/ˈsentə ɒv enˈlɑːdʒmənt/ | centre d'agrandissement |
Where is the enlargement centre?
- A logo is enlarged around a point away from the origin. Multiplying its coordinates alone puts it in the wrong place.
- This lesson studies centre of enlargement 位似中心: The point from which each point's displacement is multiplied by a scale factor.
Choose the mathematical structure
- A translation adds a vector. A reflection reverses signed perpendicular distance from a mirror line. A rotation needs a centre, angle and direction. For enlargement from C, use new P=C+k(P-C).
- State the allowed inputs and units before calculating. An equation should express the relationship, not just record a calculator entry.
Which description correctly defines centre of enlargement? · Laquelle des descriptions définit correctement le centre de dilatation ?
The point from which each point's displacement is multiplied by a scale factor. · Le point à partir duquel le déplacement de chaque point est multiplié par un facteur d'échelle.
Work through a checked case
- Check the result against the starting quantities. Substitute into the original relation, or compare the graph and numerical answer where appropriate.
For C=(1,1),P=(3,2),k=2, the image is C+2(P-C)=(5,3). With k=1/2 it is (2,1.5); with k=-2 it is (-3,-1), on the opposite side of the centre. Reflecting (3,2) in the y-axis gives (-3,2), and a 90° anticlockwise rotation about the origin gives (-2,3). Identify centre, factor, line, angle and direction as applicable.
Reflections, rotations and enlargements · Réflexions, rotations et dilatations
A translation adds a vector · Une translation ajoute un vecteur
Explain why scaling P directly would give a different enlargement. · Expliquer pourquoi l'échelle directe de P donnerait une dilatation différente.
For C=(1,1),P=(3,2),k=2, find the image x-coordinate. · Pour C=(1,1), P=(3,2), k=2, trouver l'abscisse de l'image.
Image=C+2(P-C). Its x-coordinate is 1+2(3-1)=5. · Image=C+2(P-C). Son abscisse est 1+2(3-1)=5.
Test a tempting shortcut
- A rotation needs its centre and direction, not just an angle. A negative enlargement factor places the image on the opposite side of the centre. A translation does not change orientation or size.
- When a shortcut fails, identify the assumption it breaks. Keep an exact value until the requested final rounding.
Every enlargement is centred at the origin unless its scale factor is negative. This claim is false. Explain which definition or assumption it violates.
For that enlargement, find the image y-coordinate. · Pour cette dilatation, trouver l'ordonnée de l'image.
Its y-coordinate is 1+2(2-1)=3. · Son ordonnée est 1+2(2-1)=3.
Every enlargement is centred at the origin unless its scale factor is negative. · Toute dilatation est centrée à l'origine sauf si son facteur d'échelle est négatif.
A rotation needs its centre and direction, not just an angle. A negative enlargement factor places the image on the opposite side of the centre. A translation does not change orientation or size. · Une rotation nécessite son centre et sa direction, pas seulement un angle. Un facteur de dilatation négatif place l'image de l'autre côté du centre. Une translation ne modifie ni l'orientation ni la taille.
Interpret a new situation
- Describe a transformation completely before constructing the image. Check corresponding distances and angles. For combined transformations, apply them in the stated order; they usually do not commute.
- A complete solution gives the mathematical result and explains what it means. Check that it is possible in the stated context.
Reflect (3,2) in the y-axis. Find the new x-coordinate. · Réfléchir (3,2) par rapport à l'axe des y. Trouver la nouvelle abscisse.
Reflection in the vertical axis negates x: 3 becomes -3. · Une réflexion sur l'axe vertical annule x : 3 devient -3.
Match each part of a complete solution to its purpose. · Associer chaque partie d'une solution complète à son but.
An assumption justifies the model; a check tests the result; interpretation connects it to the question. · Une hypothèse justifie le modèle ; une vérification teste le résultat ; l'interprétation le relie à la question.
Use this in your course
- 8300 · Higher · 3.4. Match the target tier and specification before assigning extensions.
- Give the method before the final answer, and use the paper's calculator and formula rules. Review a wrong answer by locating the first invalid step.
The point from which each point's displacement is multiplied by a scale factor. Choose the relationship, show the method, check its assumptions and interpret the result.