Question

triangle abc was translated according to the rule t4.5, -6.2(x, y) to form abc as shown. what are the coordinates of point c of the pre - image? (3.5, -9.2) (-2.7, -4.7) (-5.5, 3.2) (0.7, -1.3)

Explanation:

Step1: Understand the translation rule

The translation rule is $T_{4.5,- 6.2}(x,y)=(x + 4.5,y-6.2)$. To find the pre - image coordinates from the image coordinates, we need to reverse the operations. That is, if $(x',y')$ is the image coordinate and $(x,y)$ is the pre - image coordinate, then $x=x'-4.5$ and $y=y'+6.2$.

Step2: Identify the coordinates of $C'$

From the graph, the coordinates of $C'$ are $(-1,-3)$.

Step3: Calculate the coordinates of $C$

For the $x$ - coordinate of $C$: $x=-1 - 4.5=-5.5$.
For the $y$ - coordinate of $C$: $y=-3 + 6.2=3.2$.

Answer:

$(-5.5,3.2)$