The point (1,1) is the image under the translation (x,y) - (x+3,y-3). What is the preimage of this point?

Question

The point (1,1) is the image under the translation (x,y) -> (x+3,y-3). What is the preimage of this point?

freckles · Answer

(1,1)=(x+3,y-3)
means 1=x+3 and 1=y-3
what is (x,y)=(?,?)

anonymous · Answer

(1,1)?

anonymous · Answer

Wait (4,-2) Right?

freckles · Answer

so you aren't sure how to solve 1=x+3 or 1=y-3?

freckles · Answer

x+3=1 can be solved by subtracting i3 on both sides
this will isolate the variable x and therefore solved for x

freckles · Answer

x+3=1
what do you get when you subtract 3 from both sides

anonymous · Answer

Oh I see what to do now. I thought you just plugged in 1 to each equation. So the answer would be (-2,4)?

freckles · Answer

yes (-2,4) when translated by the rule (x,y)->(x+3,y-3) gives you the image (1,1)

anonymous · Answer

Okay, thank you so much!

freckles · Answer

np