Question

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

Answer 1

Answer:

(-2,4)

Step-by-step explanation:

$\text{pre-image}->\text{image}$

$(x,y)->(x+3,y-3)$

$(x,y)->(1,1)$

This implies $(x+3,y-3)=(1,1)$.

This means $x+3=1$ and $y-3=1$.

Subtract 3 on both sides for first equation: $x=1-3=-2$.

Add 3 on both sides for the second equation: $y=1+3=4$.

So the pre-image (x,y) is (-2,4) if the image is (1,1).

Let's check:

$(x,y)->(x+3,y-3)$

$(-2,4)->(-2+3,4-3)$

$(-2,4)->(1,1)$

So the solution has been checked and verified.