Rectangular Coordinate System (I) 8.49
(b) The coordinates of C are (5 , -4).
a The coordinates of B and C are different.
` C does not coincide with B.
` The claim is disagreed.
Diagram Clue
y
x
O
A(-5,-4) C
'C does not coincide
with B' means that
'C and B are different
points'.
◀
In the figure, Q(-2 , -2) is obtained when a
point P is rotated clockwise about the origin
O through 90c.
(a) Find the coordinates of P.
(b) P is reflected in the y-axis to a point R.
Cathy claims that R coincides with Q.
Do you agree? Explain your answer.
18
Instant Drill
➥ Ex 8D 24
O
x
y
Q(- 2,- 2)
The following example shows that when all the vertices of a triangle are
rotated in the same way, a new triangle can be drawn.
The figure shows a right-angled triangle JKL with vertices
J(-2 , 3), K(-3 , 1) and L(-2 , 1). J, K and L are rotated
clockwise about the origin O through 90c to Jl, Kl and
Ll respectively.
(a) Find the coordinates of Jl, Kl and Ll.
(b) Draw 3JlKlLl in the figure. Is JlLl perpendicular
to KlLl? Explain your answer.
(a) Coordinates of Jl = (,)32
Coordinates of Kl = (,)13
Coordinates of Ll = (,)12
(b)
O
-3
x
y
J
K
K'
J'
L'
L
-2 -1 1
1
2
3
2 3 4
a JlLl is a horizontal line and KlLl is a vertical
line.
` JlLl is perpendicular to KlLl.
Level 2
Example 19
Explain
O
-3
x
y
J
K L
-2 -1 1
1
2
3
2 3 4
Solution
[ Objective: Question related to rotation in a rectangular coordinate
plane.]
(2 , -2)
yes
Supp Example 19
[on P.T8.76h]