Given points a (-3; 7), b (-1; -1), c (5; 3). Determine the coordinates of point K if AB = CK

Find the coordinates of the vector AB, for this, subtract the coordinates of the starting point A from the coordinates of the end point B:

AB = ((-1 – (-3)); (-1 – 7) = (2; -8).

Since AB = CK, the coordinates of point K are equal (from the coordinates of point C, you need to subtract the coordinates of the vector CK):

((5 – 2); (3 – (-8)) = (3; 11).

Answer: the required coordinates of the point K are equal to (3; 11).