# 第二學習階段 ```Key Stage 3
Measures, Shape and Space Dimension
Learning Unit：Introduction to Coordinates
Learning Objectives ：
&middot; understand and use the rectangular and polar coordinate systems
to describe positions of points in a plane
&middot; able to locate a point in a plane by means of an ordered pair in
the rectangular coordinate system
&middot; 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
&middot; 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
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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.
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
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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.
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F
```