Rectangular Coordinate System (I) 8.43
The figure shows a line segment EF with end points
E(3 , 2) and F(1 , -1). E and F are reflected in the y-axis
to El and Fl respectively.
(a) Find the coordinates of El and Fl.
(b) Draw ElFl in the figure.
(a) Coordinates of El = (,)32 Coordinates
of Fl = (,)11--
(b)
FF'
E
E'
1
1
0 2 3
-3 -2 -1
-1
2
3 y
x
F
E
1
1
0 2 3
-3 -2 -1
-1
2
3 y
x
Level 1
Example 15
Solution
II. Reflection in a Horizontal or Vertical Line
Suppose we reflect a point P(x , y) in a horizontal line l to a new point
Pl, where the distance between P and l is a units. There are two cases.
(i) P'(x,y + 2a)
P(x,y)
m
a units
a units
After P is reflected upwards
in l, the coordinates of Pl
are (x , y + 2a).
(ii)
P'(x,y - 2a)
P(x,y)
m
a units
a units
After P is reflected downwards
in l, the coordinates of Pl are
(x , y - 2a).
Note: (a) Since PPl is a vertical line, the x-coordinates of P and Pl
are the same.
(b) Distance between P and Pl = 2a units
The figure shows a line segment CD with
end points C(4 , 2) and D(-2 , -1). C and
D are reflected in the x-axis to Cl and Dl
respectively.
(a) Find the coordinates of Cl and Dl.
(b) Draw ClDl in the figure.
15
Instant Drill
➥ Ex 8D 14
D
C
1
1
0 2 3 4
-2 -1
-1
-2
2
3 y
x
[ Objective: Question related to reflection in the x-axis or y-axis in a
rectangular coordinate plane.]
Supp Example 15
[on P.T8.76g]
Cl(4 , -2), Dl(-2 , 1)
D'
C'