Final answer:
The other two vertices of the parallelogram are found using the properties of parallelograms and the midpoint formula. Vertex B has coordinates (-2, -4) and vertex D has coordinates (-11, -8.5).
Step-by-step explanation:
The question requires finding the coordinates of the other two vertices of a parallelogram, given the intersection point of its diagonals and two of its vertices. This can be solved by using the properties of a parallelogram, specifically the fact that the diagonals of a parallelogram bisect each other. That means if we know the midpoint of the diagonals (which is the intersection point) and one endpoint of a diagonal, we can find the other endpoint because it will be symmetrically placed with respect to the midpoint.
Let's say the given vertices are A (-12, -3) and C (-3, 1.5), and the intersection point of the diagonals is M (-7, -3.5). To find vertex B, we use the fact that M is the midpoint of diagonal AC, thus:
- Bx = 2 * Mx - Ax = 2 * (-7) - (-12) = -2 - 12 = -2
- By = 2 * My - Ay = 2 * (-3.5) - (-3) = -7 + 3 = -4
So, the coordinates of vertex B are (-2, -4). Now, repeating the same process, we can find the coordinates of vertex D. Assuming vertex C has a symmetric point D with respect to M, we calculate:
- Dx = 2 * Mx - Cx = 2 * (-7) - (-3) = -14 + 3 = -11
- Dy = 2 * My - Cy = 2 * (-3.5) - 1.5 = -7 - 1.5 = -8.5
The coordinates of vertex D are (-11, -8.5). Therefore, the other two vertices of the parallelogram are B (-2, -4) and D (-11, -8.5).