Answer:
(a,b) → (a,-b) : Reflection about x axis.
(a,b) → (a, b+5) : Translation of the point by 5 units up.
(a,b) → (b,-a) : Rotation by 90 degree clockwise.
Step-by-step explanation:
Given:
The transformation of points are given as:
(a,b) → (a,-b)
(a,b) → (a, b+5)
(a,b) → (b,-a)
Now, let us consider each transformation one by one.
(1) (a,b) → (a,-b)
Here, the order of the coordinates has not changed. But, the y coordinate of the point has changed. The y coordinate was 'b' and it has changed only its sign but not value. So, it is a transformation related to reflection.
In reflection, only the sign changes. Since, the 'y' coordinate sing is reversed, so, it is a reflection about x axis.
(2) (a,b) → (a, b+5)
Here, the 'y' coordinate of the point has changed. The change is from 'b' to 'b+5'. So, 5 is added to the y coordinate. As per transformation rules, if a positive number 'C' is added to the y coordinate, then the point shifts vertically up by 'C' units. Hence, there is a translation of 5 units up here.
(3) (a,b) → (b,-a)
Here, the 'x' and 'y' coordinates interchange their values and also the new y coordinate has its sign reversed. This happens in rotation.
We know that, (x, y) → (y, –x) is true when there is rotation by 90 degree clockwise.
So, the point (a,b) → (b,-a) is rotated by 90 degree clockwise.
