Reflection
Reflection
If we stand in front of a mirror, our images come closer to the mirror and vice versa, it is known as reflection. In reflection, the mirror is represented by a line, which is called the axis of reflection. The properties of reflection are:
 Lateral inversion of each other
 Equidistant from the mirror line
 Congruent to each other
Reflection using Coordinates
By using the coordinates, we can reflect a given object about the xaxis, yaxis, line y = x, line y= x etc.
 Reflection in Xaxis: When we reflect a point across the xaxis, the x coordinate remains the same, but y coordinate is transformed into negative.
The reflection of the point (x, y) across the xaxis is the point (x,−y).
P(x, y) → P'(x, y)
or, xaxis (x, y) = (x,−y)  Reflection in Yaxis: When we reflect a point across the yaxis, then y coordinator remains the same, but the x coordinate is transformed into negative.
The reflection of the point (x, y) across the yaxis is the point (−x, y).
P(x, y) → P'(−x, y)
or, yaxis (x, y) = (−x, y)  Reflecting in the line y = x: When we reflect a point across the line y = x, the x coordinate and then y coordinate change place.
The reflection of the point (x, y) across the line y = x is the point (y, x).
P(x, y) → P'(y, x)
or, y = x (x, y) = (y, x)  Reflection in line y = −x: When we reflect a point across the line y = −x, the x coordinate and then y coordinate change places and are negated or the signs are changes.
The reflection point (x, y) across the line y = −x is the point (−y,−x)
P(x, y) → P'(−y,−x)
 The reflection of the point (x, y) across the xaxis is the point (x, −y) = P(x, y) → P'(x, y)
 The reflection of the point (x, y) across the yaxis is the point (−x, y) = P(x, y) → P'(−x, y)
 The reflection of the point (x, y) across the line y = x is the point (y, x) = P(x, y) → P'(y, x)
 The reflection of the point (x, y) across the line y = −x is the point (−y, −x) = P(x, y) → P'(−y, −x)

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