Rectangular Coordinate System (I) 8.65
36. D(-2 , 6) is rotated anticlockwise about the origin O through 90c,
and then translated to the right by 3 units to a point E.
(a) Find the coordinates of E.
(b) A point F is obtained when D is translated to the right by
3 units, and then rotated anticlockwise about the origin O
through 90c. Do E and F coincide? Explain your answer.
37. In the figure, l is a line parallel to the x-axis and passing through
the point (0 , 1).
(a) A is reflected in l to a point B. Find the coordinates of B.
(b) B is reflected in the y-axis to a point C. Find the coordinates
of C.
(c) C is translated 8 units downwards to a point D. Find the
coordinates of D.
(d) Is AD a horizontal line or a vertical line? Explain your answer.
38. In the figure, l is a line parallel to the y-axis and passing through
the point (7 , 0). S(4 , -4) is reflected in l to a point T.
(a) Find the coordinates of T.
(b) (i) T is rotated anticlockwise about the origin O through 90c
to a point U. Find the coordinates of U.
(ii) Jack thinks that the length of SU is greater than that of ST.
Do you agree? Explain your answer.
Level 3
39. A(a , -2), B(a , 3) and C(-6 , 3) are three points in a rectangular
coordinate plane. It is given that a 2 0 and AB + BC = 13 units.
(a) Find the value of a.
(b) Find the area of 3ABC.
40. P(15 , 3) and Q(15 , 15) are two points in a rectangular coordinate
plane.
(a) If P and Q are two vertices of a square, how many different
squares can be formed?
(b) Hence, find the minimum possible area of the square formed.
Explain
O
x
y
m
A(- 2,-3)
(0 ,1 )
Explain
O
x
y
(7,0)
m
S(4,-4)
Explain
Level 3 Guiding Worksheet - Supp Ex 8
4
4
5
5
5
(-3 , -2)
no
(-2 , 5)
(2 , 5)
(2 , -3)
horizontal line
(10 , -4)
(4 , 10)
yes
2
3
72 sq. units
20 sq. units
[Clue: Question 39(a)
Use 'AB + BC = 13 units' to set
up an equation in a. Hence, find
the value of a.]
[Clue: Question 40(a)
PQ may be a side or a diagonal of
the square.]