Final answer:
The coordinates of vertex B of parallelogram ABCD, with given vertices A, C, and D, are found to be (23, 14) by utilizing the property that the diagonals of a parallelogram bisect each other.
Step-by-step explanation:
The question asks to determine the coordinates of vertex B of a parallelogram ABCD given the coordinates of vertices A, C, and D. In a parallelogram, opposite sides are equal in length and parallel. To find the coordinates of B, we need to use the fact that the diagonals of a parallelogram bisect each other.
Let's denote the midpoint of the diagonal AC as M. To find M, we average the x-coordinates and the y-coordinates of A and C:
- Mx = (7 + 20)/2 = 13.5
- My = (12 + 5)/2 = 8.5
Since M is also the midpoint of BD, we can find B by using the coordinates of D:
- Bx = 2 * Mx - Dx = 2 * 13.5 - 4 = 23
- By = 2 * My - Dy = 2 * 8.5 - 3 = 14
Therefore, the coordinates of vertex B are (23, 14).