8.56 Chapter 8
Chapter Summary
Note Example
1. Rectangular Coordinate System
In a rectangular coordinate plane, if ( a , b)
are the coordinates of P, then a is called
the x-coordinate of P, and b is called the
y-coordinate of P.
Point Coordinates
O (0 , 0)
A (5 , -2)
B (-3 , 4)
C (2 , 0)
D (0 , -4)
2. Distance between Two Points
(a) For points lying on a horizontal line,
they have the same y-coordinate.
For points lying on a vertical line,
they have the same x-coordinate.
(b) For points P(p , y) and Q(q , y) with p 2 q,
PQ = p - q.
For points R(x , r) and S(x , s) with r 2 s,
RS = r - s.
x
y
B (2 ,-5)
D (-4,-1)
C (2 ,-1)
O
DC = [2 - (-4)] units = 6 units
CB = [(-1) - (-5)] units = 4 units
3. Areas of Polygons
(a) By finding the lengths of suitable horizontal
or vertical line segments, we can find the
areas of polygons.
(b) The areas of some figures can be found by
using splitting method or filling method.
Area of rectangle CDEF
= CD # CF
= (6 - 2) # (4 - 1) sq. units
= 12 sq. units
4. Transformations of Points
(a) Translation of a point P(x , y)
Translation by
n units
Coordinates of
the image
to the right (x + n , y)
to the left (x - n , y)
upwards (x , y + n)
downwards (x , y - n)
x
y
B (8 ,4)
C (8 ,-2)
A (3 ,4 )
O
5 units
6 units
A(3 , 4) is translated 5 units to the right to a
point B, and B is translated 6 units downwards
to a point C. Then
coordinates of B = (3 + 5 , 4) = (8 , 4)
coordinates of C = (8 , 4 - 6) = (8 , -2)
x
y
-1
-2
-3
-4
3
4
2
10 1 2 3 4
-1-2-3 5
B
C
A
D
y-axis x-axis
origin O
x
y F(2,4 ) E (6 ,4 )
C (2 ,1 ) D (6 ,1 )
O Studying
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