Question

the image of a figure is shown. what are the coordinates of x in the pre - image of the figure if the rule that created the image was t - 5.2, 1.4(x, y)?

Explanation:

Step1: Identify the translation rule

The translation rule is $T_{ - 5.2,1.4}(x,y)=(x - 5.2,y + 1.4)$. To find the pre - image coordinates from the image coordinates, we need to reverse the operation. So if $(x',y')$ are the image coordinates and $(x,y)$ are the pre - image coordinates, then $x=x'+5.2$ and $y=y' - 1.4$.

Step2: Determine the image coordinates of $X'$

From the graph, the coordinates of $X'$ are $(-1,2)$.

Step3: Calculate the pre - image coordinates of $X$

For the $x$ - coordinate of the pre - image: $x=-1 + 5.2=4.2$.
For the $y$ - coordinate of the pre - image: $y=2-1.4 = 0.6$.

Answer:

$(4.2,0.6)$