Question

finding a pre - image. 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 $t_{-5.2,1.4}(x,y)$? $x = square$

Explanation:

Step1: Understand the translation rule

The translation rule $T_{ - 5.2,1.4}(x,y)$ means a translation of $-5.2$ units in the $x$ - direction and $1.4$ units in the $y$ - direction. To find the pre - image, we need to reverse the translation. So we use the inverse rule $T_{5.2,-1.4}(x',y')$ where $(x',y')$ are the coordinates of the image point.

Step2: Identify the coordinates of $X'$

From the graph, the coordinates of $X'$ are $(0,2)$.

Step3: Apply the inverse translation rule

Let $(x,y)$ be the coordinates of the pre - image of $X$. Using the inverse translation rule, we have $x=x'+5.2$ and $y = y'-1.4$. Substituting $x' = 0$ and $y'=2$ into the equations: $x=0 + 5.2=5.2$ and $y=2-1.4 = 0.6$.

Answer:

$(5.2,0.6)$