Reflection

Reflection

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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:

  1. Lateral inversion of each other
  2. Equidistant from the mirror line
  3. Congruent to each other

Reflection using Co-ordinates

By using the coordinates, we can reflect a given object about the x-axis, y-axis, line y = x, line y= x etc.

  • Reflection in X-axis: When we reflect a point across the x-axis, the x co-ordinate remains the same, but y co-ordinate is transformed into negative.
    The reflection of the point (x, y) across the x-axis is the point (x,−y).
    P(x, y) → P'(x, -y)
    or, x-axis (x, y) = (x,−y)

  • Reflection in Y-axis: When we reflect a point across the y-axis, then y co-ordinator remains the same, but the x co-ordinate is transformed into negative.
    The reflection of the point (x, y) across the y-axis is the point (−x, y).
    P(x, y) → P'(−x, y)
    or, y-axis (x, y) = (−x, y)

  • Reflecting in the line y = x: When we reflect a point across the line y = x, the x co-ordinate and then y co-ordinate 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 co-ordinate and then y co-ordinate 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 x-axis is the point (x, −y) = P(x, y) → P'(x, y)
  • The reflection of the point (x, y) across the y-axis 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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shivam

what is reflection

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