Because we were not given any specific point to start off with. I choose (2,2), which is shown in red as 1.
We translate it 2 times.
a) (x+5)(y+3) = (2+5)(2+3) = (7,5) is our new point (shown in brown as 2)
Translation process shown in yellow.
b) (x-4)(y+2) = (7-4)(5+2) = (3,7) is our final point (shown in orange as 3)
Note that we use the 2nd point for the second translation as required.
Translation process shown in lime.
We can therefore determine from the picture below that you can use the translation (x+1)(y+5), which the translation process is shown in blue.
Proof: (x+1)(y+5) = (2+1)(2+5) = (3,7)
Now let's do it again, except we do the second translation first and the first translation last.
c) (x-4)(y+2) = (2-4)(2+2) = (-2,4) is our new point (shown in purple as 4)
Translation process shown in pink.
d) (x+5)(y+3) = (-2+5)(4+3) = (3,7) is our final point (shown in orange as 3)
Translation process shown in dark blue.
Same rules as (b). Notice how the final point is still the same? Therefore it makes no difference.
Hope I helped a lot :P
We translate it 2 times.
a) (x+5)(y+3) = (2+5)(2+3) = (7,5) is our new point (shown in brown as 2)
Translation process shown in yellow.
b) (x-4)(y+2) = (7-4)(5+2) = (3,7) is our final point (shown in orange as 3)
Note that we use the 2nd point for the second translation as required.
Translation process shown in lime.
We can therefore determine from the picture below that you can use the translation (x+1)(y+5), which the translation process is shown in blue.
Proof: (x+1)(y+5) = (2+1)(2+5) = (3,7)
Now let's do it again, except we do the second translation first and the first translation last.
c) (x-4)(y+2) = (2-4)(2+2) = (-2,4) is our new point (shown in purple as 4)
Translation process shown in pink.
d) (x+5)(y+3) = (-2+5)(4+3) = (3,7) is our final point (shown in orange as 3)
Translation process shown in dark blue.
Same rules as (b). Notice how the final point is still the same? Therefore it makes no difference.
Hope I helped a lot :P
