8.66 Chapter 8
41. The coordinates of a point A are (-2 , 7). A is translated 4 units to
the right to a point B. B is reflected in the x-axis to a point C. D is
obtained when B is rotated about the origin O through 180c.
(a) Find the coordinates of B, C and D.
(b) What kind of quadrilateral is ABCD?
(c) Find the perimeter of ABCD.
42. A point P is rotated anticlockwise about the origin O through 90c
to a point Q. Q is reflected in the y-axis to a point R. R is rotated
anticlockwise about the origin O through 90c to a point S(-4 , -6).
(a) Find the coordinates of P, Q and R.
(b) What kind of quadrilateral is PQRS?
(c) Find the area of PQRS.
Cross-topic Questions
43. The figure shows the triangle ABC. BC passes through the origin O
and AC cuts the y-axis at point D.
(a) Find the area of 3ABC.
(b) If the area of trapezium ABOD is 75% of that of 3ABC, find
the coordinates of D.
44. P(12 , 5) undergoes two translations to reach a new point R. If the
x-coordinate and y-coordinate of R are 25% and 40% greater than
the x-coordinate and y-coordinate of P respectively, describe the
possible translations.
45. The figure shows a circle with centre A. B is a point on the circle.
(a) Find the radius of the circle.
(b) Find the area of the circle.
(Take r = 3.14.)
46. The figure shows a circle whose centre G lies on the x-axis. The
circle passes through the origin. The circumference of the circle is
18.84 units.
(a) Find the radius of the circle.
(Take r = 3.14.)
(b) Find the coordinates of G.
A(-4,6)
C(4,2)
D
B(-4,-2)
y
x
O
A(4,2)
B(-1,2) y
x
O G
y
x
O
5
5
5
5
5
5
Challenging Worksheet 8
[Clue: Question 42
(a) Let (a , b) be the coordinates
of P. Find the coordinates of
Q, R and S in terms of a and
b. Since S(-4 , -6) is given,
the values of a and b can be
found. Hence, the coordinates
of P, Q and R will be found.
(b) Check if any sides of PQRS
are horizontal or vertical.
Hence, determine what kind
of quadrilateral PQRS is.]
Cross-Topic Worksheet S1
B(2 , 7), C(2 , -7), D(-2 , -7)
P(4 , -6), Q(6 , 4), R(-6 , 4)
32 sq. units
(0 , 4)
P is first translated to the right by 3 units, and then translated
upwards by 2 units to R. (or other reasonable answers)
5 units
78.5 sq. units
3 units
(-3 , 0)
36 units
100 sq. units
rectangle
trapezium
[Clue: Question 41(b)
Check if any sides of ABCD
are horizontal or vertical.
Hence, determine what kind of
quadrilateral ABCD is. ]