Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

6. Coordinates, Symmetry and Transformation

Exercise 6A Conventional Questions  Exam Tips

1. Refer to the figures below.
No need to
do this
question.
Fig. I Fig. II Fig. III
(a) Which of the figures have reflectional symmetry? Write down the
number of axes of reflectional symmetry for each of these figures.
(b) Which of the figures have rotational symmetry? Write down the
number of folds of rotational symmetry for each of these figures.

2. The slope of the straight line passing through A(2 , −5) and B(−4 , k) is
−4.
3
(a) Find the value of k.
(b) Find the distance between A and B.

3. The straight line L cuts the x-axis and the y-axis at P(2 , 0) and Q(0 , 6)
respectively. 3. (b) Do not take
 x1 − x 2 y1 − y 2 
(a) If the straight line L′ is perpendicular to L, find the slope of L′.  ,  as the
 2 2 
(b) If M is the mid-point of PQ, find the coordinates of M. mid-point formula.

4. The rectangular coordinates of the point A are ( 2 3 , −2). If A is No need towrite

4. First dodown thisthe rectangular
coordinates of B.
reflected in the x-axis to B, find the polar coordinates of B. question.

5. In a polar coordinate system, O is the pole. The polar coordinates of the

points A, B, C and D are (8 , 22°), (10 , 112°), (8 , 202°) and
(15 , 292°) respectively. No need to
(a) Are A, O and C collinear? Explain your answer. 5. (a) Consider ∠AOC.
Explain do this
(b) Find the length of CD. question.
(c) Find the area of the quadrilateral ABCD.

6. In a polar coordinate system, O is the pole. The polar coordinates of the

points A and B are (k , 87°) and (12 , 177°) respectively, where k is a
positive constant. It is given that AB = 13.
Explain (a) Is △OAB a right-angled triangle? Explain your answer.
No need to do this
6. (a) It is incorrect to use Pythagoras’
question.
theorem to find the value of k
(b) Find the perimeter of △OAB. and use this result to prove that
△OAB is a right-angled triangle.
(c) Let C be a point in the polar coordinate system such that
∠BOC = 25° and OC = OB. Find two possible polar coordinates of
C.

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 Name: ____________________ Class: __________( ) Date: __________
7. In the figure, the coordinates of the point A are (6 , 4). A is rotated
anticlockwise about the origin O through 90° to B. C is the mid-point of
AB.
y

A(6 , 4)

x
O

(a) Find the coordinates of C.

Explain (b) Is OC perpendicular to AB? Explain your answer. 7. (b) Point out whether the product of
the slopes of OC and AB is −1.
Explain (c) David claims that △OAC is an isosceles right-angled triangle. Do Then, draw a conclusion.

you agree? Explain your answer.

8. In the figure, the coordinates of the point A are (3 , 6). A is rotated

clockwise about the origin O through 90° to B. C is the reflection image
of B with respect to the y-axis.
y

A(3 , 6)

x
O

(a) Write down the coordinates of B and C.

Explain (b) Is AC perpendicular to OB? Explain your answer.
(c) A is translated vertically to D such that the area of △BCD is 30. 8. (c) Note that D can lie vertically
above or below B.
Find the possible coordinates of D.

9. In the figure, the coordinates of the points A and B are (–4 , 5) and
(2 , –4) respectively. A is rotated clockwise about the origin O through
90° to C. B is rotated clockwise about the origin O through 90° to D.
y

A(–4 , 5)

x
O
B(2 , –4)

(a) Write down the coordinates of C and D.

Explain (b) Is AC parallel to DB? Explain your answer. 9. (b) Point out whether the slopes of
AC and DB are the same. Then,
(c) If C is translated horizontally to E such that ∠ABE = 90°, find the draw a conclusion.

coordinates of E.

© Oxford University Press 2012 W06-2

 Name: ____________________ Class: __________( ) Date: __________

Junior Secondary Foundation Topics Supplement

6. Coordinates, Symmetry and Transformation

Exercise 6B MC Questions 6. The coordinates of the points A, B and C are

1. The polar coordinates of the points A and B are (2 , –1), (7 , –2) and (k , k) respectively. If
No need (7 , 118°) and (24 , 208°) respectively. Find the AC = BC, find the value of k.
to do this distance between A and B. A. 2 C. 6
question. A. 17 C. 25 B. 4 D. 8
B. 23 D. 31
7. The coordinates of the points A and B are (a , 6)
and (–5 , b) respectively. If the coordinates of
2. If the straight line L passes through A( 3 , 0)
the mid-point of AB are (–4 , 1), find the value
No need and B(0 , −1), then the inclination of L is
to do this of b.
A. 30°. C. 60°.
question. A. –4 C. 3
B. 45°. D. 150°.
B. –3 D. 4

3. If the polar coordinates of the point P are

8. Which of the following statements about a
(2 , 60°), then the rectangular coordinates of P
regular 10-sided polygon are true?
are
I. The number of folds of rotational
A. ( 3 , 1). No need symmetry is 10.
B. (1 , 3 ). to do this II. The number of axes of reflectional
C. (− 3 , 1). question. symmetry is 5.
D. (1 , − 3 ). No need
III. Each interior angle is 144°.
to do this
A. I and II only
4. If the point A(5 , –6) is rotated clockwise about question.
B. I and III only
the origin through 270°, find the coordinates of
C. II and III only
the image of A.
D. I, II and III
A. (–6 , –5)
B. (–5 , 6) 9. The vertices of the right-angled triangle ABC
C. (5 , 6) are A(–2 , 5), B(0 , 0) and C(a , 4), where
D. (6 , 5) ∠ABC = 90°. Find the value of a.
A. 5 C. 12
5. The rectangular coordinates of the point A are B. 10 D. 15
(1 , 1). If A is rotated about the origin through
180° to A′, find the polar coordinates of A′. 10. The coordinates of the point A are (–6 , 2). A is
A. (1 , 225°) rotated clockwise about the origin through
No need 270° to B. C is the reflection image of B with
B. (1 , 315°)
to do this
C. ( 2 , 225°) respect to the y-axis. Find the distance between
question.
D. ( 2 , 315°) A and C.
A. 32 C. 96
B. 80 D. 128

© Oxford University Press 2012 W06-3

 Name: ____________________ Class: __________( ) Date: __________
11. In the figure, the coordinates of the point A are 15.
No need
(–2 , –5). The horizontal line L passes through
to do this
the point (0 , 1). If A is rotated anticlockwise question.
O
about the origin O through 90° to B, find the
If the plane figure above is rotated clockwise
coordinates of the reflection image of B with
about the point O through 270°, which of the
respect to the line L.
y following is its image?
A. (–5 , 0)
A. O C.
B. (–5 , 3) (0 , 1) O
L
C. (5 , 3) x
O
D. (5 , 4)

A
B. D.

12. The coordinates of the points A, B and C are

(–5 , 4), (–1 , 8) and (7 , –5) respectively. If B O O

is translated vertically to D such that A, D and

16. The figure shown is formed by 1 regular
C are collinear, find the distance translated by
octagon and 8 equilateral triangles. 4 of the
B.
equilateral triangles are shaded. Find the
A. 1 C. 7
number of folds of rotational symmetry of the
B. 5 D. 9
figure.
13. Which of the following triangles have A. 2 No need
reflectional symmetry? B. 4 to do this
I. II. III. C. 6 question.
No need
D. 8
to do this 13 13 18
12 13
question.
12 10 10 17. In the figure, the slopes of the straight lines L 1 ,
L 2 , L 3 and L 4 are m 1 , m 2 , m 3 and m 4
A. I and II only C. II and III only respectively. If L 1 ⊥L 3 and L 2 ⊥L 4 , which of
B. I and III only D. I, II and III the following must be true?
I. m1 < m3 y
14. L2 L3
II. m3 < m4
III. m 1 m 3 = –1 L1 L4
No need A. I and II only x
to do this B. I and III only
O
question. C. II and III only
In the figure, the two 5-sided polygons show
D. I, II and III
A. a dilation transformation.
B. a reflection transformation.
C. a rotation transformation.
D. a translation transformation.

© Oxford University Press 2012 W06-4