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In Geometry, transformation means changing the appearance of an object. There are many ways in which this can be done viz translation, reflection, rotation etc.

Reflection in math definition
Reflection is a transformation in which a geometric figure is reflected across a line, creating a mirror image. Each point in the object appears at an equal distance on the opposite side of the line. This line is called the line of reflection.

The line of reflection is always perpendicular to the lines linking corresponding points in the original object and the reflected image. It also bisects these lines.

Terms related to reflection of shape
Let us understand some of the terms that are frequently used along with the reflection function:

Preimage - this term is used to refer to the original object
Image - this term is used to refer to the object after it has been reflected.

Properties of a reflection

The reflection is the same size as the original image.

Depending on the position of the axis of reflection, a reflection could be a horizontal reflection, vertical reflection or a diagonal reflection.

Reflection math examples

Reflection of a point

In order to reflect a point along a given axis of reflection, perform the following steps:
1. First draw a perpendicular line from the point to the line of reflection
2. Now measure the distance of the point from the line of reflection
3. Mark a point at the same distance on the other side of the line of reflection. This is the reflected point. The reflection of a point A is usually referred to as A’.

Reflection of a line segment

In order to reflect a line along a given axis of reflection, perform the following steps:
1. First draw a perpendicular line from each end point of the line segment to the line of reflection
2. Now measure the distance of the end points from the line of reflection
3. Mark points at the same distance on the other side of the line of reflection.
4. Join the two endpoints on the other side of the line of reflection. This is the reflected line segment. The reflection of a line segment AB is usually referred to as A’B’.

Reflection of a shape

In order to reflect a shape along a given axis of reflection, perform the following steps:
1. For each vertex of the given shape, measure the distance of the vertex from the axis of reflection
2. Now, measure the same distance on the other side of the axis and place a dot.
3. Once you have done this for all the corners of the shape, you can now join the dots to form the reflected object. The reflection of a triangle ABC is referred to a A’B’C’.

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