8.54 Chapter 8
Level 2
19. A point A is translated 3 units to the right to B and then 8 units
downwards to C(-2 , -1). Find the coordinates of A.
20. In the figure, l is a horizontal line passing through P(2 , 1). B is the
image when a point A(0 , 4) is reflected in l.
(a) Find the coordinates of B.
(b) L is a vertical line passing through P. C is the image when B is
reflected in L. Find the coordinates of C.
21. It is given that A(a + 2 , 3) is reflected in the x-axis to B(-2 , b + 3).
(a) Find the values of a and b.
(b) A is transformed to B through a translation. Describe the
translation.
22. It is given that C(c - 2 , 4) is reflected in the y-axis to D(5 , 2 - d).
(a) Find the values of c and d.
(b) C is rotated about the origin O through 180c to a point E. Find
the length of DE.
23. In the figure, l is a line passing through M(0 , -2) and is parallel to
the x-axis. E(e - 3 , 2) is reflected in the line l to F(-4 , f - 2).
(a) Find the distance between E and l.
(b) Find the values of e and f.
24. In the figure, the point D is obtained when a point C is rotated
clockwise about the origin O through 270c.
(a) What are the coordinates of C?
(b) C is reflected in the y-axis to a point E. Kelvin claims that E
coincides with D. Do you agree? Explain your answer.
25. A(-3 , -1) and B(-3 , -6) are reflected in the x-axis to Al and Bl
respectively.
(a) Find the coordinates of Al and Bl.
(b) Rachel claims that AlBl is longer than AB. Do you agree?
Explain your answer.
➥ Example 13
y
x
O
LP(2,1)
A(0,4)
m
➥ Example 16
x
y
m
M(0 ,- 2)
O
5
5
10
10
-5 -5
-10
-10 y
x
O
D
Explain
➥ Example 18
Explain
1
2
2
2
4
4
4
(-5 , 7)
(0 , -2)
(4 , -2)
a = -4, b = -6
c = -3, d = -2
(-10 , -5)
Al(-3 , 1), Bl(-3 , 6)
A is translated 6 units downwards to B.
8 units
4 units
e = -1, f = -4
no
no