Page 203 - ICSE Math 7

To draw the reflection of a point with respect to a line P

Let P be a point whose reflection is to be drawn with respect to line AB.
From point P, draw a perpendicular to AB which meets AB at Q. Produce A Q
PQ and cut QP' = QP on it. P' is the reflection of point P with respect to B
line AB. P'

To draw the reflection of a point in x-axis
While finding the reflection of a point in Y
x-axis, x-axis is considered as a plane mirror. P(x, y)
Let P(x, y) be a point whose reflection is y Maths Info
P'(x, –y) where PP' is perpendicular to x-axis x
such that PQ = P'Q. Thus, when a point X' O Q X Point (x, 0) lies on the x-axis and
is reflected in x-axis, the sign of its ordinate is –y hence is an invariant point.
changed. Example: Y' P'(x, – y)

(a) reflection of (6, –7) in x-axis is (6, 7).
(b) reflection of (–5, 2) in x-axis is (–5, –2).

To draw the reflection of a point in y-axis

While finding the reflection of a point in Y
y-axis, y-axis is considered as a plane mirror. P' (–x, y) P(x, y) Maths Info
Let P(x, y) be a point whose reflection is y Q y Point (0, y) lies on the y-axis and
P'(–x, y) where PP' is perpendicular to y-axis –x O x hence is an invariant point.
such that PQ = P'Q. Thus, when a point is X' X
reflected in y-axis, the sign of its abscissa is Y'
changed. Examples:
(a) reflection of (–3, 2) in y-axis is (3, 2).

(b) reflection of (–7, –9) in y-axis is (7, –9).

To draw the reflection of a point in origin
Let P(x, y) be a point whose reflection in origin is P'(–x, –y). Thus, when Y
a point is reflected in origin, the signs of both its components are changed. P(x, y)
Example:
(a) reflection of (5, –6) in origin is (–5, 6). X' O X
(b) reflection of (–4, 3) in origin is (4, –3). P' (–x, – y)

(c) reflection of (–2, –3) in origin is (2, 3). Y'

To draw the reflection of a line segment with respect to a line A

Let AB be a line segment whose reflection is to be drawn with respect to line B
l. From point A, draw a perpendicular to l which meets l at C. Produce AC C D
and cut CA' = CA. Similarly, from B draw a perpendicular to l which meets l
l at D. Produce BD and cut DB' = DB. Join A' and B' to get the required B'
reflection A'B' of line segment AB with respect to line l. A'

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