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Textbook: Transformations (Term 3)
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Page 1 GrADe 6: MATheMATiCS [TerM 3] 247 Unit 6 t r Ansform Ations 6.1 Rotations, reflections and translations The red figure on this bead mat is a translation of the purple figure. The red figure on this bead mat is a rotation of the purple figure. The red figure on this bead mat is a reflection of the purple figure. Maths_English_LB_Grade6_Book.indb 247 2016/12/15 4:21:45 PM Page 2 GrADe 6: MATheMATiCS [TerM 3] 247 Unit 6 t r Ansform Ations 6.1 Rotations, reflections and translations The red figure on this bead mat is a translation of the purple figure. The red figure on this bead mat is a rotation of the purple figure. The red figure on this bead mat is a reflection of the purple figure. Maths_English_LB_Grade6_Book.indb 247 2016/12/15 4:21:45 PM 248 UNiT 6: TrANSFOrMATiONS Mzwi traced the figure on the right onto brown cardboard. He then cut it out, and used it as a template to draw diagrams consisting of two figures each. To draw the above diagram, Mzwi first put the template in the position on the left, and traced around it in black. Then he reflected the template to the position on the right, and traced around it in red. 1. The diagram below shows the template on the black position. (a) Can the template be moved to fit on the red position just by translating it? (b) How must the template be moved to fit on the red position? Maths_English_LB_Grade6_Book.indb 248 2016/12/15 4:21:46 PM Page 3 GrADe 6: MATheMATiCS [TerM 3] 247 Unit 6 t r Ansform Ations 6.1 Rotations, reflections and translations The red figure on this bead mat is a translation of the purple figure. The red figure on this bead mat is a rotation of the purple figure. The red figure on this bead mat is a reflection of the purple figure. Maths_English_LB_Grade6_Book.indb 247 2016/12/15 4:21:45 PM 248 UNiT 6: TrANSFOrMATiONS Mzwi traced the figure on the right onto brown cardboard. He then cut it out, and used it as a template to draw diagrams consisting of two figures each. To draw the above diagram, Mzwi first put the template in the position on the left, and traced around it in black. Then he reflected the template to the position on the right, and traced around it in red. 1. The diagram below shows the template on the black position. (a) Can the template be moved to fit on the red position just by translating it? (b) How must the template be moved to fit on the red position? Maths_English_LB_Grade6_Book.indb 248 2016/12/15 4:21:46 PM GrADe 6: MATheMATiCS [TerM 3] 249 2. The diagrams below show the brown template on the black position. In each case state whether the template should be rotated, reflected or translated to move it to fit on the red position. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Maths_English_LB_Grade6_Book.indb 249 2016/12/15 4:21:46 PM Page 4 GrADe 6: MATheMATiCS [TerM 3] 247 Unit 6 t r Ansform Ations 6.1 Rotations, reflections and translations The red figure on this bead mat is a translation of the purple figure. The red figure on this bead mat is a rotation of the purple figure. The red figure on this bead mat is a reflection of the purple figure. Maths_English_LB_Grade6_Book.indb 247 2016/12/15 4:21:45 PM 248 UNiT 6: TrANSFOrMATiONS Mzwi traced the figure on the right onto brown cardboard. He then cut it out, and used it as a template to draw diagrams consisting of two figures each. To draw the above diagram, Mzwi first put the template in the position on the left, and traced around it in black. Then he reflected the template to the position on the right, and traced around it in red. 1. The diagram below shows the template on the black position. (a) Can the template be moved to fit on the red position just by translating it? (b) How must the template be moved to fit on the red position? Maths_English_LB_Grade6_Book.indb 248 2016/12/15 4:21:46 PM GrADe 6: MATheMATiCS [TerM 3] 249 2. The diagrams below show the brown template on the black position. In each case state whether the template should be rotated, reflected or translated to move it to fit on the red position. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Maths_English_LB_Grade6_Book.indb 249 2016/12/15 4:21:46 PM 250 UNiT 6: TrANSFOrMATiONS 3. In the patterns below, a green template is shown on the first position. In each case state whether the template should be rotated, reflected or translated to move it from one position to the next. (a) (b) (c) (d) Maths_English_LB_Grade6_Book.indb 250 2016/12/15 4:21:46 PM Page 5 GrADe 6: MATheMATiCS [TerM 3] 247 Unit 6 t r Ansform Ations 6.1 Rotations, reflections and translations The red figure on this bead mat is a translation of the purple figure. The red figure on this bead mat is a rotation of the purple figure. The red figure on this bead mat is a reflection of the purple figure. Maths_English_LB_Grade6_Book.indb 247 2016/12/15 4:21:45 PM 248 UNiT 6: TrANSFOrMATiONS Mzwi traced the figure on the right onto brown cardboard. He then cut it out, and used it as a template to draw diagrams consisting of two figures each. To draw the above diagram, Mzwi first put the template in the position on the left, and traced around it in black. Then he reflected the template to the position on the right, and traced around it in red. 1. The diagram below shows the template on the black position. (a) Can the template be moved to fit on the red position just by translating it? (b) How must the template be moved to fit on the red position? Maths_English_LB_Grade6_Book.indb 248 2016/12/15 4:21:46 PM GrADe 6: MATheMATiCS [TerM 3] 249 2. The diagrams below show the brown template on the black position. In each case state whether the template should be rotated, reflected or translated to move it to fit on the red position. (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) Maths_English_LB_Grade6_Book.indb 249 2016/12/15 4:21:46 PM 250 UNiT 6: TrANSFOrMATiONS 3. In the patterns below, a green template is shown on the first position. In each case state whether the template should be rotated, reflected or translated to move it from one position to the next. (a) (b) (c) (d) Maths_English_LB_Grade6_Book.indb 250 2016/12/15 4:21:46 PM GrADe 6: MATheMATiCS [TerM 3] 251 6.2 Describing patterns The design with triangles on the above wall is often used in Ndebele art. There are many rotations, reflections and translations in this design. 1. Which of these arrangements form part of the above design, and which do not? (a) (b) (c) (d) 2. In each case below, state whether the grey triangle is a translation, rotation or reflection of the black triangle. (a) (b) (c) (d) Maths_English_LB_Grade6_Book.indb 251 2016/12/15 4:21:46 PMRead More
FAQs on Textbook: Transformations (Term 3)
| 1. What are the different types of transformations in geometry? |  |
Ans. The main types of transformations in geometry are translations, rotations, reflections, and dilations. A translation slides a shape from one position to another without changing its size or orientation. A rotation turns a shape around a fixed point, while a reflection flips a shape over a line. Dilation changes the size of a shape while maintaining its proportions.
| 2. How can I identify a transformation in a geometric figure? | |
Ans. To identify a transformation in a geometric figure, look for changes in position, size, or orientation. For translations, check if the shape has moved without changing. For rotations, identify the angle and direction of the turn. For reflections, find the line of symmetry where the shape has been flipped. For dilations, compare the size of the original shape to the new shape to see if it has been enlarged or reduced.
| 3. What is the importance of transformations in real life? | |
Ans. Transformations are important in real life as they help us understand and model various situations. For example, architects use transformations to design buildings, while graphic designers apply them to create logos and animations. Understanding transformations also aids in problem-solving and reasoning in fields like engineering and computer graphics.
| 4. How do I perform a reflection transformation on a coordinate plane? | |
Ans. To perform a reflection transformation on a coordinate plane, first identify the line of reflection, which can be the x-axis, y-axis, or any other line. Then, for each point of the shape, find its corresponding point on the opposite side of the line, the same distance away. For instance, if reflecting over the y-axis, change the sign of the x-coordinate while keeping the y-coordinate the same.
| 5. Can transformations change the shape of an object? | |
Ans. No, transformations such as translations, rotations, reflections, and dilations do not change the shape of an object, but they can change its position or size. In a dilation, the shape may get larger or smaller, but it maintains its proportions and angles, meaning it is still similar to the original shape.
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