You could also refer to some notes on coordinate geometry published before.
Things to remember:
- In A Co-ordinate plane, there are two axis:
and
.
- Any point on a plane can be represented as
- When you state the coordinate of a point, the abscissa (
coordinate) precedes the ordinate (
coordinate).
- Co-ordinate of origin is
- Co-ordinate of a point of
- Co-ordinate of a point of
Reflection:
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 also
Reflection in line
In the adjoining diagram, you see that point reflection is
. The
does not change, only the
changes.
become
when reflected on
.
In a generic form, we can say that the reflection of on
is
.
Reflection in line
Similarly, you see that point reflection is
. The
does not change, only the
changes.
become
when reflected on
.
In a generic form, we can say that the reflection of on
is
Reflection in the origin:
In the above diagram, you would see that in reflection in Origin, both and
change.
become
when reflected in the origin.
Invariant Point:
Any point that remains unaltered under a given transformation is called invariant. For example:
- Reflection of
in
would remain same as
- Reflection of
in
would remain same as
- Reflection of
in
would remain same as
Remember, in case of an Invariant point, the point itself is its own image. Similarly, every point in a like
is reflected in
itself , the point is invariant.