Question

If the range of the coordinate transformation (, ) = (−2,−3 +1) is (4, −2), (2, −5), (−6, 4), what is the domain?

Answer 1

Consider the below figure attached with this question.

Given:

The transformation is:

$f(x,y)=(-2x,-3y+1)$

The range is (4,-2), (2, −5), (−6, 4).

To find:

The domain of the transformation.

Solution:

We have,

$f(x,y)=(-2x,-3y+1)$

For the point (4,-2),

$(-2x,-3y+1)=(4,-2)$

On comparing both sides, we get

$-2x=4$

$x=\dfrac{4}{-2}$

$x=-2$

And,

$-3y+1=-2$

$-3y=-2-1$

$-3y=-3$

$y=\dfrac{-3}{-3}$

$y=1$

So, the domain of (4,-2) is (-2,1).

Similarly,

For the point (2,-5),

$(-2x,-3y+1)=(2,-5)$

On comparing both sides, we get $x=-1,y=2$. So, the domain of (2,-5) is (-1,2).

For the point (-6,4),

$(-2x,-3y+1)=(-6,4)$

On comparing both sides, we get $x=3,y=-1$. So, the domain of (-6,4) is (3,-1).

So, the domain of the given transformation is (-2, 1), (-1, 2), (3, -1).

Therefore, the correct option is A.