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)? x = (-7.2, 3.4) (1.2, 6.6) (3.2, 0.6) (9.2, -0.4)

Explanation:

Step1: Understand the translation rule

The translation rule $T_{ - 5.2,1.4}(x,y)$ means that to get the image coordinates, we subtract 5.2 from the $x$ - coordinate and add 1.4 to the $y$ - coordinate of the pre - image. Let the coordinates of $X$ in the pre - image be $(x,y)$ and the coordinates of $X'$ (from the graph) be $( - 2,2)$. Then we have the equations: $x-5.2=-2$ and $y + 1.4=2$.

Step2: Solve for $x$

From $x-5.2=-2$, we add 5.2 to both sides of the equation. So $x=-2 + 5.2=3.2$.

Step3: Solve for $y$

From $y + 1.4=2$, we subtract 1.4 from both sides of the equation. So $y=2-1.4 = 0.6$.

Answer:

$(3.2,0.6)$