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Transformations

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The document describes 9 diagrams showing geometric shapes, transformations, and properties. Diagram 1 shows a point P' as the image of point P under a transformation M. The following diagrams and questions involve reflections, rotations, enlargements, similarities, and constructions involving congruent or corresponding parts of geometric figures. The key information is describing various geometric transformations and identifying corresponding or congruent elements of figures related by transformations.

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10. Transformations 1. In Diagram 1, P' is the image of P under transformation M. y 12 10 P' 8 6 4 P 2 2 4 6 8 10 12 x DIAGRAM 1 Describe in full transformatiom M. [PMR 2004] Answer :
2. Diagram 2 in the answer space shows polygon ABCDEF and straight line PQ drawn on a grid of equal squares. Starting from the line PQ, draw polygon PQRSTU which is congruent to polygon ABCDEF. [PMR 2004] Answer : DIAGRAM 2 F A E D C B P Q 3. Diagram 3 in the answer space shows two quadrilaterals, ABCD and A'B'C'D', drawn on a grid of equal squares. A'B'C'D' is the image of ABCD under a reflection. On the diagram in the answer space, draw the axis of reflection. Answer : [PMR 2005] A B C D D' A' C' B' DIAGRAM 3
4. Diagram 4 shows three triangles, P,Q and R, which are drawn on a Cartesian plane. [PMR 2005] y 10 8 R 6 P 4 2 Q -4 -2 0 2 4 6 x DIAGRAM 4 (a Q is the image of P under a rotation of 90°. State (i) the direction of the rotation, (ii) the coordinates of the centre of rotation. (b) R is the image of P under transformation M. Describe in full transform M. Answer : (a) (i) (ii) (b)
5. Diagram 5 shows two polygons, H and H', drawn on a grid of equal squares with sides of 1 unit. [PMR 2006] H' H DIAGRAM 5 H' is the image of H under transformation L. Describe in full transformation L. Answer : 6. Diagram 6 in the answer space shows object P and straight line MN drawn on a grid of equal squares. On Diagram 6 in the answer space, draw the image of P under a reflection in the straight line MN. [PMR 2006] Answer : M P N DIAGRAM 6
7. Diagram 7 in the answer space shows quadrilateral PQRS. R'S' is the image of RS Under a reflection in the straight line MN. On Diagram 7 in the answer space, complete the image of quadrilateral PQRS.[PMR 2007] Answer : N S' S R' R P Q M Diagram 7
8. Diagram 8 in the answer space shows two quadrilaterals, JKLM and J'K'L'M' , drawn on a grid of equal squares. J'K'L'M' is the image of JKLM under an enlargement. On Diagram 8 in the answer space , mark P as the centre of enlargement. [PMR 2007] Answer : K' K J J' M L M' L' Diagram 8
9. In Diagram 9, triangles EFG and HIJ are similar. [PMR 2007] E J I 65° 65° F 40° G 75° H Diagram 9 State (a) the angle in triangle HIJ which corresponds to ∠ FEG. (b) the side in triangle HIJ which corresponds to the side EF in triangle EFG. Answer : (a) (b)
Transformations

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Transformations

  • 1. 10. Transformations 1. In Diagram 1, P' is the image of P under transformation M. y 12 10 P' 8 6 4 P 2 2 4 6 8 10 12 x DIAGRAM 1 Describe in full transformatiom M. [PMR 2004] Answer :
  • 2. 2. Diagram 2 in the answer space shows polygon ABCDEF and straight line PQ drawn on a grid of equal squares. Starting from the line PQ, draw polygon PQRSTU which is congruent to polygon ABCDEF. [PMR 2004] Answer : DIAGRAM 2 F A E D C B P Q 3. Diagram 3 in the answer space shows two quadrilaterals, ABCD and A'B'C'D', drawn on a grid of equal squares. A'B'C'D' is the image of ABCD under a reflection. On the diagram in the answer space, draw the axis of reflection. Answer : [PMR 2005] A B C D D' A' C' B' DIAGRAM 3
  • 3. 4. Diagram 4 shows three triangles, P,Q and R, which are drawn on a Cartesian plane. [PMR 2005] y 10 8 R 6 P 4 2 Q -4 -2 0 2 4 6 x DIAGRAM 4 (a Q is the image of P under a rotation of 90°. State (i) the direction of the rotation, (ii) the coordinates of the centre of rotation. (b) R is the image of P under transformation M. Describe in full transform M. Answer : (a) (i) (ii) (b)
  • 4. 5. Diagram 5 shows two polygons, H and H', drawn on a grid of equal squares with sides of 1 unit. [PMR 2006] H' H DIAGRAM 5 H' is the image of H under transformation L. Describe in full transformation L. Answer : 6. Diagram 6 in the answer space shows object P and straight line MN drawn on a grid of equal squares. On Diagram 6 in the answer space, draw the image of P under a reflection in the straight line MN. [PMR 2006] Answer : M P N DIAGRAM 6
  • 5. 7. Diagram 7 in the answer space shows quadrilateral PQRS. R'S' is the image of RS Under a reflection in the straight line MN. On Diagram 7 in the answer space, complete the image of quadrilateral PQRS.[PMR 2007] Answer : N S' S R' R P Q M Diagram 7
  • 6. 8. Diagram 8 in the answer space shows two quadrilaterals, JKLM and J'K'L'M' , drawn on a grid of equal squares. J'K'L'M' is the image of JKLM under an enlargement. On Diagram 8 in the answer space , mark P as the centre of enlargement. [PMR 2007] Answer : K' K J J' M L M' L' Diagram 8
  • 7. 9. In Diagram 9, triangles EFG and HIJ are similar. [PMR 2007] E J I 65° 65° F 40° G 75° H Diagram 9 State (a) the angle in triangle HIJ which corresponds to ∠ FEG. (b) the side in triangle HIJ which corresponds to the side EF in triangle EFG. Answer : (a) (b)