The points A(1, -2, 4), B(3, 5, 7), C(4, 6, 8) are three of four vertices of parallelogram ABCD. Determine the coordinates of vertex D
Could someone please tell me to go about solving this question. Thanks a lot.
D (5,7,9)
To determine the coordinates of vertex D of the parallelogram ABCD, we can use the properties of a parallelogram.
1. Find the vectors representing the sides of the parallelogram:
- Vector AB: Subtract the coordinates of point A from the coordinates of point B: AB = (3-1, 5-(-2), 7-4) = (2, 7, 3).
- Vector AC: Subtract the coordinates of point A from the coordinates of point C: AC = (4-1, 6-(-2), 8-4) = (3, 8, 4).
2. Add the vector AB to the coordinates of point C to find point D:
- Point D = C + AB = (4, 6, 8) + (2, 7, 3) = (6, 13, 11).
Therefore, the coordinates of vertex D are (6, 13, 11).