Question

I need help with this question... the correct answer choice

Answer 1

We have a translation T that transform (-2, 3) into (3,-1).

We can think of the translation as adding "a" units to the x-coordinate and "b" units to the y-coordinate.

So we can express it as:

`(x^(\prime),y^(\prime))=(x+a,y+b)`

As the translated point is (3,-1) and the original point is (-2,3), we should have:

`\begin{gathered} (3,-1)=(-2+a,3+b) \\ 3=-2+a\longrightarrow a=3+2=5 \\ -1=3+b\longrightarrow b=-1-3=-4 \end{gathered}`

Knowing "a" and "b", we can describe the transformation as:

`(x^(\prime),y^(\prime))=(x+5,y-4)`

Then, for the point (4,2) the translation will result in:

`\begin{gathered} (x^(\prime),y^(\prime))=(4+5,2-4) \\ (x^(\prime),y^(\prime))=(9,-2) \end{gathered}`

Answer: (9,-2) [Fourth option]