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 $T_{4.5,-6.2}(x,y)$ means that to get the image - point, we add 4.5 to the x - coordinate and subtract 6.2 from the y - coordinate of the pre - image point. Let the coordinates of point C in the pre - image be $(x,y)$ and the coordinates of $C'$ be $(x',y')$. 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: Solve for the x - coordinate of C

We know that $x'=x + 4.5$. Substituting $x'=-1$ into the equation, we get $-1=x + 4.5$. Solving for $x$:
$x=-1 - 4.5=-5.5$

Step4: Solve for the y - coordinate of C

We know that $y'=y-6.2$. Substituting $y'=-3$ into the equation, we get $-3=y-6.2$. Solving for $y$:
$y=-3 + 6.2 = 3.2$

Answer:

$(-5.5,3.2)$