\( D \) and \( R \) are points on a polygon. \( D^{\prime} \) and \( R^{\prime} \) are the points under a translation. Find \( R^{\prime} \) \( D(6,-10) \) \( D^{\prime}(15,-9) \) \( R(12,-1) \)

To find the coordinates of \( R' \) under the same translation that maps \( D \) to \( D' \), follow these steps: 1. **Determine the Translation Vector:** The translation moves point \( D(6, -10) \) to \( D'(15, -9) \). The translation vector \((a, b)\) can be found by subtracting the coordinates of \( D \) from \( D' \): \[ a = 15 - 6 = 9 \] \[ b = -9 - (-10) = 1 \] So, the translation vector is \((9, 1)\). 2. **Apply the Translation to Point \( R \):** To find \( R' \), add the translation vector to the coordinates of \( R(12, -1) \): \[ R'_x = 12 + 9 = 21 \] \[ R'_y = -1 + 1 = 0 \] Therefore, \( R' \) is at \((21, 0)\). **Answer:** \( R^{\prime} = (21,\ 0) \)