Question

rectangle efgh is translated according to the rule ( t_{-5,9}(x,y) ). if the coordinates of the pre - image of point h are ( (-2,-3) ), what are the coordinates of ( h )?
( (7,-8) )
( (-7,6) )
( (3,-12) )
( (2,1) )

Explanation:

Step1: Analyze the translation rule

The translation rule \(T_{-5,9}(x,y)\) means \(x\) - coordinate is changed as \(x-5\) and \(y\) - coordinate is changed as \(y + 9\).

Step2: Apply the rule to the pre - image coordinates

Given the pre - image of point \(H\) is \((-2,-3)\).
For the \(x\) - coordinate: \(x=-2\), after translation \(x'=-2-5=-7\).
For the \(y\) - coordinate: \(y = - 3\), after translation \(y'=-3 + 9=6\).

Answer:

\((-7,6)\) (corresponding to the second option)