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Reflection of Geometrical Figures

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Reflection in Geometrical Figures

The reflection of a geometrical figure means the formation of the image of the figure after reflecting the figure about the line of reflection.

Properties of Reflection

  1. There should be equal distance between the geometrical figure and its image from the line of reflection.
  2. The areas of the geometrical figure and its image are equal.
  3. The appearance of the image of a figure is opposite to figure.

Reflection of geometrical figures using coordinates

Here, we can find the co-ordinates of the images of geometrical figures formed due to the reflection by x-axis and y-axis separately. In this case, x-axis and y-axis are called the axis of reflection.

  1. X-axis as the axis of reflection
    When a geometrical figure is reflected about x-axis as the axis of reflection, the x-coordinate of the image remains the same and the sign of y-coordinate of the image as changed.

  2. Y-axis as the axis of reflection
    When a geometrical figure is reflected about y-axis as the axis of reflection, the sign of x-coordinate of the image is changed but the y-coordinate of the image remains the same.




  • Properties of Reflection

    1. There should be equal distance between the geometrical figure and its image from the line of reflection.
    2. The areas of the geometrical figure and its image are equal.
    3. The appearance of the image of a figure is opposite to figure.
.

Very Short Questions

Solution:

S

A(2,-2)\(\rightarrow\)A’(-2,-2)

B(5,3)\(\rightarrow\)B’(-5,3)

C(1,4)\(\rightarrow\)C’(-1,4)

So, the coordinates of the vertices of image \(\triangle\)A’B’C’ are A(-2,-2), B(-5,3) and C(-1,4).

Solution:

S

A(-2,3)\(\rightarrow\)A’(-2,-2)

B(2,1)\(\rightarrow\)B’(2,-1)

C(4,4)\(\rightarrow\)C’(4,-4)

So, the coordinates of the vertices of image \(\triangle\)A’B’C’ are A(-2,-3), B(2,-1) and C(4,-4).

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  • What coordinates of image do we get from the points (2, 6) under the reflection about the x-axis?

    (-6, 2)
    (-2, -6) 
    (2, -6)
    (-2, 6) 
  • What coordinates of image do we get from the points (-3, 8) under the reflection about the x-axis?

    (-8, -3)
    (-3, 8)
    (-8, 3)
    (-3, -8)
  • What coordinates of image do we get from the points (7, -4) under the reflection about the x-axis?

    (4, 7)
    (7, 4)
    (-4, -7)
    (-4, 7)
  • What coordinates of image do we get from the points (-5, -9) under the reflection about the x-axis?

    (-9, 5)
    (5, 9)
    (-9, -5)
    (-5, 9)
  • What coordinates of image do we get from the points (0, -6) under the reflection about the x-axis?

    (-6, 0)
    (-0, 6)
    (6, 0)
    (0, 6)
  • What coordinates of image do we get from the points (5, 3) under the reflection about the y-axis?

    (-3, 5)
    (5, 3)
    (-3, -5)
    (-5, 3)
  • What coordinates of image do we get from the points (4, -7) under the reflection about the y-axis?

    (7, -4)
    (-4, 7)
    (-7, -4)
    (-4, -7)
  • What coordinates of image do we get from the points (-9, 6) under the reflection about the y-axis?

    (6, -9)
    (9, 6)
    (-6, 9) 
    (-9, -6)
  • What coordinates of image do we get from the points (-2, -5) under the reflection about the y-axis?

    (-2, -5)
    (2, -5)
    (5, 2)
    (-5, -2)
  • What coordinates of image do we get from the points (-3, 0) under the reflection about the y-axis?

    (-0, -3)
    (3, -0)
    (3, 0)
    (0, 3)
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