\( A \) and \( D \) are points on a polygon. \( A^{\prime} \) and \( D^{\prime} \) are the points under a translation. Find \( D^{\prime} \). \( A(-2,-15) \) \( A^{\prime}(0,-10) \) \( D(-10,10) \)

To determine the coordinates of \( D^{\prime} \) after the translation, we first need to identify the translation vector applied to point \( A \). Given: - \( A(-2, -15) \) is translated to \( A^{\prime}(0, -10) \). Let's find the translation vector \((h, k)\): \[ \begin{align*} -2 + h &= 0 \quad \Rightarrow \quad h = 2 \\ -15 + k &= -10 \quad \Rightarrow \quad k = 5 \end{align*} \] So, the translation vector is \((2, 5)\). Now, apply this translation to point \( D(-10, 10) \): \[ D^{\prime} = D + (2, 5) = (-10 + 2, 10 + 5) = (-8, 15) \] **Answer:** After the translation, \( D^{\prime} \) is at the point \( (-8,\ 15) \).