Congruency, Enlargement and Combined Transformations

Question 9: (a)  Diagram 8.1 shows point K ( 3, 2 ) marked on a Cartesian plane.Diagram 8.1  The transformation T is a translation ( − 2 3 ) .   The transformation R is a reflection in the line y = 3. State the coordinates of the image of point K under each of … Read more

Question 7:Diagram shows the point J(1, 2) and quadrilaterals ABCD and EFGH, drawn on a Cartesian plane.(a) Transformation U is a rotation of 90o, clockwise about the centre O.Transformation T is a translation  ( 2 3 )  Transformation R is a reflection at the line x = 3.State the coordinates of the image of point J under each of the following transformations:(i) RU,(ii) TR.(b) EFGH is the … Read more

Question 5:(a) Diagram below shows two points, M and N, on a Cartesian plane.Transformation T is a translation (  3 −1 ) and transformation R is an anticlockwise rotation of 90o about the centre (0, 2).(i) State the coordinates of the image of point M under transformation R.(ii) State the coordinates of the image of … Read more

Question 3: (a) Transformation P is a reflection in the line x = m. Transformation T is a translation ( 4 − 2 ) . Transformation R is a clockwise rotation of 90o about the centre (0, 4). (i) The point (6, 4) is the image of the point ( –2, 4) under the transformation P. State the … Read more

  Question 1: (a) Transformation T is a translation ( − 4 2 ) and transformation P is an anticlockwise rotation of 90oabout the centre (1, 0). State the coordinates of the image of point (5, 1) under each of the following transformation: (i) Translation T, (ii) Rotation P, (iii) Combined transformation T2. (b) Diagram below shows three … Read more

5.4 Solving Problems Involving Transformations Example: The diagram below shows the triangles ABC, SQT and PQR. (a) Transformation T is a translation (  5 −2 )   Transformation P is a reflection in the straight line y = 7. State the coordinates of the image of point A under each of the following transformations: (i) Transformation T, (ii) … Read more

5.3d Describing the Combination of Two Transformations Given the Object and the Image   Example 1: In the diagram above, triangle KLM is the image of triangle ABC under the combined transformations VW. Describe in full, the transformation W and the transformation V. Solution: Figure ABC → W→ Figure KB’C’ → V → Figure KLM W = … Read more

5.3c Stating the Coordinates of the Image of a Point under a Combined Transformation   1. The coordinates of the image of a point, K, under the combined transformation AB can be determined by the following steps.   Step 1: Determine the coordinates of K’, the image of K, under the first transformation, B. Step 2: … Read more

5.3b Determining the Image of an Object under Combination of (a) Two Enlargements or (b) an Enlargement and an Isometric Transformation   1. Enlargement is a transformation where all points of an object on a plane move from a fixed point at a constant ratio.   2. The fixed point is called the centre of enlargement and … Read more

5.3a Determining the image of an object under the combination of two isometric transformations 1. Translations, reflections and rotations are isometric transformations.   2. In an isometric transformation, the shape and the size of the image is the same as the object.   3. For two transformations, A and B, (a) Combined transformation AB represents transformation B followed … Read more