Let's first identify the given composition of isometries.
R_(x=0)∘ T_(<-12,-6>)
Reflection across x= 0
Translation 12 units left and 6 units down
To complete this composition of isometries, we first perform the translation and then the reflection.
Translation
To translate the point (11,-5) twelve units left, we have to subtract 12 from the x-coordinate. Then, to move the point (11,-5) six units down, we have to subtract 6 from the y-coordinate.
(x,y) → (x-12,y-6)
Let's start with this.
Reflection
To complete the reflection, we have to reflect both of the coordinates of the point (11,-5) on the opposite side of the y-axis in a way such that the distance from the points to the y-axis remains the same.
Final Composition of Isometries
The final composition of the given isometries is the combination of the translation and the reflection.
