8.38 Chapter 8
From Class Activity 8.4, we can see that:
For any point P(x , y),
(a) the coordinates of the image after P is
translated n units upwards are (x , y + n),
(b) the coordinates of the image after P is
translated n units downwards are (x , y - n).
(x,y - n)
P(x,y)
(x,y + n)
n units
n units
Note: For translation upwards or downwards, the point P and its image lie
on the same vertical line. Therefore, their x-coordinates are the same.
(a) M(-2 , -1) is translated 8 units to the right to a
point N. Find the coordinates of N.
(b) P(4 , 1) is translated 6 units downwards to a point Q.
Find the coordinates of Q.
(c) D(7 , -2) is translated 3 units upwards to a point E
and then translated 4 units to the left to a point F.
Find the coordinates of F.
(a) Diagram Clue
y
x
O
N
M(-2,-1)
8 units
Coordinates of N
= (-2 + 8 , -1)
= (, )61(b)
Diagram Clue
y
x
O
Q
P(4,1)
6 units
Coordinates of Q
= (4 , 1 - 6)
= (, )45(c)
Diagram Clue
y
x
O
F
E
D(7,-2)
3 units
4 units
Coordinates of E
= (7 , -2 + 3)
= (7 , 1)
Coordinates of F
= (7 - 4 , 1)
= (,)31
Level 1
Example 12
Solution
[ Objective: Question related to translation in a rectangular coordinate
plane.]
N25 When the transformation
involves translations only,
the order is not important.
e.g. In Example 12(c), if D is
translated 4 units to the left
and then translated 3 units
upwards, the image is still
point F.
N25
Supp Example 12
[on P.T8.76f]