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Key Stage 3 Measures, Shape and Space Dimension Learning Unit：Introduction to Coordinates Learning Objectives ： · understand and use the rectangular and polar coordinate systems to describe positions of points in a plane · able to locate a point in a plane by means of an ordered pair in the rectangular coordinate system · describe intuitively the effects of transformation such as translation, reflection with respect to lines parallel to x-axis, y-axis and rotation about the origin through multiples of 90 on points in coordinate planes · calculate areas of figures that can be cut into or formed by common 2-D rectilinear figures Programme Title: Coordinate Geometry Programme Objectives 1. Recognize the use of rectangular coordinates to describe the position of a point. 2. Understand the relation between the x-coordinates of any two points on a horizontal line, and between the y-coordinates of any two points on a vertical line of a rectangular coordinate plane. 3. Investigate the fundamental knowledge of geomertry, including distance between two points, perimeters and areas of simple 2-D rectilinear figures in the rectangular coordinate system. 4. Recognize the use of polar coordinates to describe the position of a point. 5. Explore and describe intuitively the effects of transformation such as translation, reflection with respect to lines parallel to x-axis, y-axis and rotation about the origin through multiples of 90 on points in coordinate -1- planes. Programme Content The programme starts with the situation where a visitor checks the location of a place on a map by referring to the index references to reveal the use of an ordered pair to describe the position of a point on a plane. It also uses a seating plan of a classroom as a daily life example to illustrate that an ordered pair, (x,y), can be used to denote the position of a student. It is highlighted that (x,y) and (y,x) are referring to different positions. The rectangular coordinate system is introduced. Some geometrical properties on a rectangular coordinate plane are explored: a point is located with its coordinates, relation between the coordinates of two points on a straight line, distance between two points, perimeters and areas of simple 2-D rectilinear figures. Through the illustration of the location of a position of an object by a radar system in navigation and the weather forecast of a typhoon, the idea of the polar coordinate system and its representations is introduced. The last part of the programme leads the exploration on the effects on the coordinates of a point under various forms of transformation. Worksheet Answers 1. 2. 3. 4. 5. 6. D(-6, 7), E(-6,-5), F(7,-5) CD = 13 units, CF = 12 units, EB = 10 units, DA = 5 units ∆CBF= (12 x 3)/2= 18 sq. units ∆ABE = (7 x 10)/2= 35 sq. units ∆CDA= (5 x 13)/2= 32.5 sq. units ∆ABC= 13 x 12 - 18 - 35 - 32.5 = 70.5 sq. units -2- Key Stage 3 ETV Programme《Coordinate Geometry》 Worksheet Y D C (7,7) A (-6,2) X E B (4,-5) 1. Write down the coordinates of D, E and F. 2. Find the distance between (a) C and D (b) C and F (c) E and B (d) D and A 3. Find the area of ∆CBF. 4. Find the area of ∆ABE. 5. Find the area of ∆CDA. 6. Find the area of ∆ABC. -3- F