The vector CD is directed in the same direction as the vector AB and the length of the vector CD

The vector CD is directed in the same direction as the vector AB and the length of the vector CD is equal to the root of 225 find the coordinates of the point D if a (4.9) b (1.5) and c (-1.7).

Find the coordinates of the vector AB: ((1 – 4); (5 – 9)) = (-3; -4). Then its modulus is:

| AB | = √ (-3) ^ 2 + (-4) ^ 2 = 5.

Coordinates of the unit vector (ort) | AB | equal: (-3/5; -4/5).

Since the vectors AB and CD have the same direction, the coordinates of their unit vectors coincide, then the coordinates of the vector | CD | are equal: (-3 * √225 / 5; -4 * √225 / 5) = (-15; -20).

Knowing the coordinate of point C (-1; 7), we get the coordinates of point D: ((-15 + (-1)); (- 20 + 7)) = (-16; -13).

Answer: point D has coordinates (-16; -13)