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

Explanation:

Step1: Recall translation rule

The translation rule $T_{ - 5.2,1.4}(x,y)=(x - 5.2,y + 1.4)$. We want to find the pre - image of a point. Let the coordinates of the pre - image of $X'$ be $(x,y)$ and the coordinates of $X'$ be $(a,b)$. Then $a=x - 5.2$ and $b=y + 1.4$, so $x=a + 5.2$ and $y=b - 1.4$.

Step2: Assume coordinates of $X'$

Let's assume the coordinates of $X'$ are $( - 2,5)$. Then $x=-2 + 5.2=3.2$ and $y=5 - 1.4 = 0.6$.

Answer:

$(3.2,0.6)$