Question

quadrilateral abcd has been through a translation of (x,y)→(x + 4,y - 7). where would the pre - image point d have been located prior to the translation? o (-1,2) o (-1,-12) o (7,-2) o (7,-12)

Explanation:

Step1: Recall translation rule reversal

To find the pre - image, we reverse the translation. Given $(x,y)\to(x + 4,y - 7)$, the reverse is $(x,y)\to(x - 4,y+7)$.

Step2: Assume coordinates of $D'$

Let's assume the coordinates of $D'$ are $(3,-5)$ (by observing the grid, if we assume the bottom - left corner of the grid is the origin $(0,0)$ and each square represents one unit).

Step3: Apply reverse - translation

For the $x$ - coordinate of the pre - image of $D$: $x=3 - 4=-1$. For the $y$ - coordinate of the pre - image of $D$: $y=-5 + 7=2$.

Answer:

$(-1,2)$