Dilation transformation for Class 8 geometry pptx

This ppt is about dilation for grade 8 student mathematics from geometry.

1. Dilation(Dilatation) Transformation

2. Dilation A dilation is a transformation in which a figure is enlarged or reduced with respect to a fixed point R called the center of dilation. In this Picture, ▲PQS is pre-image and ▲P’Q’S’ is the image . Dilatation can be of two type: Expansion - When the size of an object is increased. Contraction - When the size of an object is decreased

3. The Scale Factor Scale factor denoted by k or r , which is the ratio of the lengths of the corresponding sides of the image and the preimage . Size of shape after dilatation depends on scale factor . Scale factor = From the diagram, scale factor (k) = or   The image is enlarged if the scale factor is more than 1 (k > 1). The image is contracted if the scale factor is less than 1 (0< k <1). The image remains the same if the scale factor is 1 (k = 1)

4. How to Calculate the Scale Factor in Dilation? Scale factor = Considering dimension PR: Scale factor = = k = 3 Therefore, the scale factor in this dilation is 3  

5. Questions

6. What is the scale factor if the trapezoid ABCD is dilated ro A’B’C’D’?

7. Applying Scale Factor (Steps of Dilation) Dilate the shape ABCD from dilation center Q with Scale factor =   Join one of the vertices and measure the distance between dilatation Centre and the vertices. Multiply the distance by scale factor to get image vertices = 15.2 x = 7.6 Mark the point at 7.6 (B’)  

8. Repeat for all vertices and join image vertices to get the dilated shape( Image can be form by joining all the points ( A’B’C’D’)

9. You Do

10. Identification of dilatation If a shape is the dilated image of the original, then the lines drawn from vertices intersect at one point (called dilatation centre ). Example: To Identify if Triangle HIJ is enlargement of triangle EFG   Join each corresponding vertices to find if they intersect at a point Since the lines do not intersect, Triangle HIJ is not a dilated image of triangle EFG

11. Practice Questions

12. You Do a) You are making your own photo stickers. Your photo is 4 inches by 4 inches. The image on the stickers is 1.1 inches by 1.1 inches. What is the scale factor of this dilation? Join the classroom : tcthtuue

13. b) You are using a magnifying glass that shows the image of an object as six times the object’s actual size. Determine the length of the image of the spider seen through the magnifying glass.

14. Dilation With Software ( Geogebra 5) Dilation can be perform using Geo- Gebra

15. Combined Transformation

16. Recall the meaning of all four types of transformation and properties image after each transformation

17. What transformation takes shape D into shape E?

18. Triangle ABC is transformed to A’B’C’ with following sequences of transformation Transformation Sequence A -Reduce by scale factor using vertex A as dilation centre -reflect the shape along line BC Transformation Sequence B( alter above sequence) -reflect the shape along line BC -reduce by scale factor using vertex A as dilation centre  

19. You Do Reflect the triangle over the line y=1 and then translate 4 units right. After completing the transformation, alter the sequence and cross check images. Write your observation

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