13. The point \( A=(8,-3), \quad B(-17,6) \) and \( C(-30,-1) \) are given. Find the coordinates of \( D \), if \( \overrightarrow{A B}=-\overrightarrow{C D} \).

To find the coordinates of point \( D \), we first calculate the vector \( \overrightarrow{AB} \). The vector from \( A \) to \( B \) is: \[ \overrightarrow{AB} = B - A = (-17, 6) - (8, -3) = (-17 - 8, 6 - (-3)) = (-25, 9) \] According to the problem statement, we have: \[ \overrightarrow{AB} = -\overrightarrow{CD} \] Thus: \[ -\overrightarrow{CD} = (-25, 9) \] So, we can find \( \overrightarrow{CD} \): \[ \overrightarrow{CD} = (25, -9) \] Now, we can find point \( D \) using the coordinates of point \( C \): \[ D = C + \overrightarrow{CD} = (-30, -1) + (25, -9) = (-30 + 25, -1 - 9) = (-5, -10) \] Therefore, the coordinates of point \( D \) are \( D = (-5, -10) \).