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 )? ( \bigcirc (7, -8) ) ( \bigcirc (-7, 6) ) ( \bigcirc (3, -12) ) ( \bigcirc (2, 1) )

Explanation:

Step1: Understand Translation Rule

The translation rule \( T_{-5, 9}(x, y) \) means we subtract 5 from the \( x \)-coordinate and add 9 to the \( y \)-coordinate of the pre - image. So the formula for the image \( (x', y') \) from the pre - image \( (x, y) \) is \( x'=x - 5 \) and \( y'=y + 9 \).

Step2: Identify Pre - image Coordinates

The pre - image of point \( H \) has coordinates \( (-2,-3) \), so \( x=-2 \) and \( y = - 3 \).

Step3: Calculate \( x' \)

Substitute \( x=-2 \) into \( x'=x - 5 \): \( x'=-2-5=-7 \)

Step4: Calculate \( y' \)

Substitute \( y = - 3 \) into \( y'=y + 9 \): \( y'=-3 + 9=6 \)

Answer:

\((-7,6)\)