Construction - 10

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Reflection in a line

In Physics, we study reflection and the image formed by a plane mirror. We specially notice two properties of the image:

(i) The image is as much behind the mirror as the object is in front of it.

(ii) The mirror is the perpendicular bisector of the line joining the image and the object.

XY is the mirror.

P is the object and I the image.

XY is the perpendicular bisector of PI.

(a) Reflection of a point in a line

A line XY and a point P outside it.

The reflection of P in XY.

(i) Construct a perpendicular from P to XY to meet XY at M.

(ii) Produce PM to P' such that PM = P'M.

Then, P' is the image of P in XY.

If point P is on XY, then P itself is the image.

(b) Reflection of a line in a line

A line XY and a line AB.

The reflection of AB in XY.

(i) From A, construct AM ^ XY and produce it.

(ii) Obtain point A' (the reflection of A in XY) on the other side of XY, so that AM = A'M.

(iii) Similarly, from B, construct BN ^ XY and produce it.

(iv) Obtain point B' (the reflection of B in XY) on the other side of XY, so that BN = B'N.

(v) Join A'B'.

(vi) \A'B' is the reflection of AB in XY.

(c) Reflection of a point through a point

A point A and a point M.

We are required to construct the reflection of point A through a point M.

(i) Join AM and produce it.

(ii) Obtain point A' on the line so that AM = A'M.

(iii) Then A' is the image of A in point M.

(d) Reflection of a line through a point

A line AB and a point O.

We are required to reflect AB through O.

(i) Join AO and produce it to A', so that AO = A'O.

(ii) Similarly, join BO and produce it to B', so that BO = B'O.

(iii) Join A'B'.

Then A'B' is the image of AB in O.