In Geometry, reflection is one of the four types of transformations. The four basic transformations are
 Translation
 Reflection
 Rotation
 Dilation or Resizing
In this article, let’s discuss the meaning of Reflection in Maths, reflections in the coordinate plane and examples in detail.
Reflection Definition
In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction. In reflection, translation may also take place because of its changes in the position. Here, the original image is called preimage, and its reflection is called image. The representation of preimage and image are ABC and A’B’C’ respectively. The reflection transformation may be in reference to the coordinate system (X and Yaxis).
Reflections in the Coordinate Plane
The reflection transformation may be in reference to X and Yaxis.
Reflection over Xaxis
When a point is reflected across the Xaxis, the xcoordinates remain the same. But the Ycoordinates are transformed into its opposite signs.
Therefore, the reflection of the point (x, y) across Xaxis is (x, y).
Reflection over Yaxis
When a point is reflected across the Yaxis, the Ycoordinates remain the same. But the Xcoordinates are transformed into its opposite signs.
Therefore, the reflection of the point (x, y) across Yaxis is (x, y).
Reflection over Y = X
When a point is reflected across the line y = x, the xcoordinates and ycoordinates change their place. Similarly, when a point is reflected across the line y = x, the xcoordinates and ycoordinates change their place and are negated.
Therefore,
The reflection of the point (x, y) across the line y = x is (y, x).
The reflection of the point (x, y) across the line y = – x is (y, x).
Reflection in a Point
A reflection point occurs when a figure is constructed around a single point known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.
Reflection in origin (0, 0)
In the coordinate plane, we can use any point as the point of reflection. The most commonly used point is “origin”.
Example
Let ABC be the triangle, and the coordinates are A(1,4), B(1,1), and C(5,1). After the point of reflection in origin, the preimage ABC is transformed into A’B’C’. When you draw a line segment connecting the points A and A’, the origin should be the midpoint of the line.
Therefore,
The point of reflection in origin (0, 0), the image of the point (x, y) is (x, y).
Hence, the coordinates of the triangle A’B’C are A’(1,4), B’(1,1), and C’(5,1).
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