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 \( H^{\prime} \) ? \( (7,-8) \) \( (-7,6) \) \( (3,-12) \) \( (2,1) \)

To find the coordinates of point \( H' \) after the translation \( T_{-5,9}(x, y) \), we apply the translation rule to the coordinates of point \( H \) which are \( (-2, -3) \). The translation rule works as follows: - \( x' = x + (-5) \) - \( y' = y + 9 \) Applying this to point \( H \): 1. For the x-coordinate: \[ x' = -2 - 5 = -7 \] 2. For the y-coordinate: \[ y' = -3 + 9 = 6 \] Thus, the coordinates of \( H' \) are \( (-7, 6) \). So the correct answer is: \( (-7,6) \)