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You could also refer to some notes on coordinate geometry published before.

Things to remember:

  1. In A Co-ordinate plane, there are two axis: x-axis and y-axis .
  2. Any point on a plane can be represented as (x, y)
  3. When you state the coordinate of a point, the abscissa ( x coordinate) precedes the ordinate (y  coordinate).
  4. Co-ordinate of origin is (0, 0)
  5. Co-ordinate of a point of x-axis \ is \  (x,0)
  6. Co-ordinate of a point of y-axis \ is \  (y,0)

 

 

EG5Reflection:CG1

When any object is placed in front of a mirror, its image is formed at the same distance behind the mirror as the object is front of it.

Here OP = OP' also \angle BOP = \angle AOP' = 90^{\circ}

 

Reflection in line y-axis
In the adjoining diagram, you see that point A's  reflection is A' . The y-coordinate  does not change, only the x-coordinate  changes. (7, 8)  become (-7, 8)  when reflected on y-axis .

In a generic form, we can say that the reflection of (x,y) CG2 on y-axis is (-x,y) .

Reflection in line x-axis

Similarly, you see that point P's reflection is P' . The x-coordinate  does not change, only the y-coordinate  changes. (5, 4) become (5, -4) when reflected on y-axis .

In a generic form, we can say that the reflection of (x,y) on x-axis is (x,-y)

Reflection in the origin:

In the above diagram, you would see that in reflection in Origin, both x-coordinate  and y-coordinate  change. (3, 3) become (-3, -3) when reflected in the origin.

 

EG3Invariant Point:

Any point that remains unaltered under a given transformation is called invariant. For example:

  1. Reflection of (5,0)  in x-axis  would remain same as (5,0)
  2. Reflection of (0,5)  in y-axis  would remain same as (0,5) 
  3. Reflection of (0,0)  in origin  would remain same as (0,0) 

Remember, in case of an Invariant point, the point itself is its own image. Similarly, every point P  in a like AB  is reflected in AB  itself , the point is invariant.

 

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