TRANSFORMATION GEOMETRY TRANSLATION - a horizontal or vertical ‘slide’ from one position to another - the object DOES NOT change its shape or size EXAMPLE: Left & Right x co-ordinate Up & Down y co-ordinate Point A has been translated to Point A’. It moved 2 units right and 1 unit up. The rule for this translation is (x + 2, y + 1). Point B has been translated to Point B’. It moved 4 units left and 3 units down. The rule for this translation is (x – 4, y – 3). Point C has been translated to Point C’. It moved 3 units left and 2 units up. The rule for this translation is (x - 3, y + 2). Left & Down minus Up & Right plus ∆DEF has been translated to ∆D’E’F’. It moved 5 units right and 3 units down. The rule for this translation is (x + 5, y - 3). REFLECTION - a mirror image of a shape about a line of reflection - the object DOES NOT change its shape or size reflection about the y-axis y: stays the same x: changes sign reflection about the x-axis x: stays the same y: changes sign reflection about the y=x line the co-ordinates swop around (x; y) (y; x) EXAMPLE: Point A has been reflected to Point A’ about the y-axis. Point B has been reflected to Point B’ about the x-axis Point C has been reflected to Point C’ about the y=x line. ∆DEF has been reflected to ∆D’E’F’ about the y-axis. ∆GHI has been reflected to ∆G’H’I’ about the x-axis. ∆JKL has been reflected to ∆J’K’L’ about the y=x line. ENLARGEMENT AND REDUCTION - making a shape bigger or smaller EXAMPLE: ∆ABC has been enlarged to ∆A’B’C’ by a factor of 3. ∆DEF has been reduced to ∆D’E’F’ by a factor of ½. *make sure that ALL the co-ordinates were multiplied/divided TRANSFORMATION GEOMETRY NAME:____________________ Answer the questions on this page. GRADE:___________________ ____________ 1. Translate point A 6 units left and 2 units up. (2) 2. Translate point B 2 units right and 4 units down. (2) 3. Write the rule of the translation of point C. (2) 4. Determine the translations: 4.1 D(4, -7) D'(2,-4) (2) 4.2 E(0,4) E'(-4,2) (2) 5. Write down the co-ordinate if G is reflected about the x-axis. (2) 6. Write down the co-ordinate if H is reflected about the y-axis. (2) 7. Write down the co-ordinate if I is reflected about the y=x line. (2) 8. Reflect ∆JKL about the x-axis. Draw the reflected triangle. (3) 9. ∆MNO is enlarged by a factor of 3. Draw the enlarged triangle. (3) 10. ∆PQR is reduced by a factor of ½. Draw the reduced triangle. (3) TOTAL TRANSFORMATIONS: [25] GEOMETRY OF 3D SHAPES VERTEX - corner of the polyhedron EDGE - side of a polygonal face FACE - sides of the polyhedron POLYHEDRON VERTICES EDGES FACES 6 9 5 8 12 6 10 15 7 EULER'S LAW: V - E + F = 2 * if the solid's vertices, edges and faces are put in the formula and the answer equals 2, then it is a polyhedron GEOMETRY OF 3D SHAPES NAME:____________________ Answer the questions on this page. GRADE:___________________ ____________ 1. Study the polyhedrons below and complete the table. Polyhedron Vertices Edges Faces (9) 2. 3. If a solid has 12 vertices, 14 edges and 4 faces, is it a polyhedron? Make use Euler's law. (3) If a solid has 18 vertices, 17 edges and 3 faces, is it a polyhedron? Make use Euler's law. (3) TOTAL 3D SHAPES : [15] DATA HANDLING MEASURE DEFINITION HOW TO CALCULATE EXAMPLE 2, 2, 3, 5, 5, 7, 8 MEAN average 1. add all the values 2. divide by the number of values ODD number of values: 1. Arrange the values in order 2. Find the middle number MEDIAN MODE RANGE middle value EVEN number of values: 1. Arrange the values in order 2. Find the two middle numbers 3. Add them together and divide the answer by 2. Find the value that appears the the value that appears the most most. It is possible to have more than one mode. difference between the biggest and the smallest number Subtract the lowest number from the highest number 1. 2+2+3+5+5+7+8=32 2. Mean = 32 ÷ 7 = 4.57 5,7,1,3,9 1. Arrange: 1, 3, 5, 7, 9 2. Median = 5 2,6,11,7,1,9 1. Arrange: 1,2,6,7,9,11 2. Median = (6 + 7) 2 = 6.5 2, 2, 3, 5, 5, 7, 8 Mode = 2 and 5 2,6,11,7,1,9,7 Mode = 7 2,6,11,7,1,9,7 Range = 11 - 1 = 10 DATA HANDLING PART 1 NAME:____________________ Answer the questions on this page. GRADE:___________________ ____________ 1. Peter rolled a dice ten times. He wrote down the numbers that the dice landed on. Here are the numbers: 2. 3 2 4 6 3 3 4 2 5 4 a) Calculate the mean. (2) b) Calculate the median. (2) c) Calculate the range. (2) d) What is the mode? (2) A rugby team played 7 games. Here is the number of points they scored in each game. 3 5 8 9 12 12 16 Calculate the median. (2) The team played another game. They scored 11 points. Calculate the median number of points scored in these 8 games. (2) 3. The following test marks were recorded from 6 girls and 4 boys. Girls Boys 5 2 3 5 10 9 2 3 7 3 a) Write down the mode of the 10 marks. (2) b) Calculate the median mark of the boys. (2) c) Work out the range of the girls' marks. (2) d) Calculate the mean of all 10 students. (2) TOTAL DATA HANDLING PART 1: [20] REPRESENTING DATA