Question

Square ABCD was translated using the rule (x, y) → (x – 4, y + 15) to form A'B'C'D'. What are the coordinates of point D in the pre-image if the coordinates of point D’ in the image are (9, –8)?
(13, –23)
(5, 7)
(18, 1)
(–6, –4)

Answer 1

@peachpi

Answer 2

i was once told subtract the original from the spicy... to me it didnt make sense but here how it work\[\left(\begin{matrix}9 \\ -8\end{matrix}\right)-\left(\begin{matrix}-4 \\ 15\end{matrix}\right)=\left(\begin{matrix}13 \\ -23\end{matrix}\right)\]

Answer 3

As an alternative to @lynfran's method, you could also look at it as follows:

The transformation is T: (x,y) -> (x-4, y+15)
to go from ABCD to A'B'C'D'.

The inverse transformation, \(T^{-1}\) is given by:
\(T^{-1}\) : (x,y) -> (x+4, y-15)

So apply the inverse transformation to D' to get back D.

Answer 4

so, it's A?

Answer 5

yea