Question

triangle abc was translated according to the rule ( t_{4.5,-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: Recall 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 of a point \((x',y')\) (image point), we use the reverse rule \(x=x'-4.5\) and \(y=y'+6.2\).

Step2: Identify the coordinates of \(C'\)

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

Step3: Apply the reverse translation rule

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:

\((-5.5,3.2)\) (the third option)