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 $y-axis \ is \ (y,0)$

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 $OP = OP'$ 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 $(x,y)$ 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.

Invariant 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.