Page 212 - ICSE Math 8

Reflection of a point about y-axis

Consider a point A(x, y). To get its reflection
in y-axis, draw AB perpendicular to y-axis.
Produce AB, such that AB = A′B. So, the
reflection of point A(x, y) about y-axis is A′(–x,
y). Thus, when a point is reflected of y-axis, the
sign of its abscissa is changed. For example,
reflection of (5, –3) in y-axis is (–5, –3).
Y
Reflection of a point about origin

Consider a point A(x, y). To get its reflection about origin O, join AO A(x, y)
and produce upto A′, such that AO = A′O. So, the reflection of point
A(x, y) about origin is A′(–x, –y). Thus, when a point is reflected about X′ O X
origin, the signs of both its components are changed. For example,
reflection of (–4, –5) in origin is (4, 5).
A′(–x, –y)
Example 1: Find the reflection of point (1, 4) about x-axis. Y′
Solution: The reflection of point (x, y) about x-axis is (x, –y).
∴ Reflection of (1, 4) is (1, –4).
Example 2: What is the reflection of point (–2, 3) about the origin?
Solution: The reflection of point (x, y) about the origin is (–x, –y).

∴ Reflection of (–2, 3) is (2, –3).
Example 3: The coordinates of the vertices of a triangle are A(2, 4),
B(–3, 2) and C(3, 1). Find the reflection of ∆ABC about
x-axis.
Solution: Reflection of ∆ABC about x-axis is ∆A′B′C′
with A′(2, –4), B′(–3, –2) and C′(3, –1).

Rotation
Maths Info
Rotation is a transformation which rotates all the points in a plane about a
fixed point through a given angle. The fixed point about which the rotation • The shape and size of a
is made is known as the centre of rotation and the amount of rotation is geometrical figure does not
known as the angle of rotation. change after reflection and
rotation.
By convention, positive rotations go counter clockwise (anticlockwise) and • The orientation of the figure
negative rotations go clockwise. is reversed with respect to the
axis of reflection.

Rotation of a point through 180° about the origin
Consider a point A(3, 2). If the point A(3, 2) is rotated about the origin
O through an angle of 180° (clockwise or anticlockwise) it will reach
A′(–3, –2), such that OA = OA′ and ∠AOA′ = 180°. Thus, the image of a
point A(x, y) rotated about the origin through an angle of 180° is A′(–x, –y).

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