8.42 Chapter 8
In general,
for any point P(x , y),
(a) the coordinates of the image after P is
reflected in the x-axis are (x , -y),
(b) the coordinates of the image after P is
reflected in the y-axis are (-x , y).
x
y
O
P(x,y)
(x,- y)
(- x,y)
Note: When a point P is reflected in a straight line l to a new point Pl,
(a) the distance between P and l is equal to the distance between
Pl and l,
i.e. PH = PlH,
(b) PPl = l.
Quick
Example (a) P(4 , -3) is reflected in the x-axis to a point Q.
x
y
O
P(4,-3)
Q
Coordinates of Q = (,)43
(b) M(-8 , 5) is reflected in the y-axis to a point N.
x
y
O
M(-8,5)
N
Coordinates of N = (,)85
Quick Quiz
(a) A(7 , 2) is reflected in the x-axis to a point B. Find the coordinates of B.
(b) C(-6 , -1) is reflected in the y-axis to a point D. Find the coordinates of D.
H
P P'
m
When a point is reflected
in the x-axis (y-axis),
its x-coordinate
(y-coordinate) remains
the same.
N26 Remind students that P
and Q are equidistant from
the x-axis. In fact, when Q
is reflected in the x-axis, P
becomes the image of Q.
N27 Remind students that M
and N are equidistant from
the y-axis. In fact, when N
is reflected in the y-axis, M
becomes the image of N.
N26
N27
(7 , -2)
(6 , -1)