在平面直角坐标系中，平行四边形的三个顶点A，B，C的坐标分别为（-1，0），（3，0），（0，2），第四个顶点D在第一象限内．（1）求点D的坐标及四边形ABDC的面积；（2）在y轴上是否存在一点P，连接PA，PB，使S△PAB=S四边形ABDC？若存在这样一点，求出点P的坐标；若不存在，试说明理由．---**Diagram Description:** * **Type:** Geometric diagram on a 2D Cartesian coordinate plane. * **Coordinate Axes:** * A horizontal axis labeled 'x'. * A vertical axis labeled 'y'. * The intersection of the axes is the origin, labeled 'O'. * **Points:** * Point A is on the x-axis, labeled with '-1'. * Point B is on the x-axis, labeled with '3'. * Point C is on the y-axis, above the origin, labeled 'C'. * Point D is in the first quadrant, labeled 'D'. * **Segments:** Line segments connect points A and C, C and D, D and B, and A and B, forming a quadrilateral labeled ABCD. * **Labels and Annotations:** * Axis labels: x, y, O. * Point labels: A, B, C, D. * Coordinate values on axes: -1 (near A on x-axis), 3 (near B on x-axis). * **Inferred Information (based on appearance):** * Coordinates of A: (-1, 0). * Coordinates of B: (3, 0). * Coordinates of C: (0, y_C) for some y_C > 0. * The figure appears to be a parallelogram where segment AB is parallel to segment CD, and segment AC is parallel to segment BD. This indicates the vertices are likely A, B, D, C in order (parallelogram ABDC) or A, C, D, B in order (parallelogram ACDB). Based on the visual appearance, AB appears parallel to CD, and AC appears parallel to BD. This strongly suggests parallelogram ABDC. * Assuming ABDC is a parallelogram, vector AB = vector CD. Vector AB = (3 - (-1), 0 - 0) = (4, 0). Let D = (x_D, y_D). Vector CD = (x_D - 0, y_D - y_C) = (x_D, y_D - y_C). Equating the vectors gives x_D = 4 and y_D - y_C = 0, so y_D = y_C. * Coordinates of D: (4, y_C), where y_C is the y-coordinate of C. * The length of AB is 3 - (-1) = 4. The length of CD is also 4. **Textual Information:** The image contains only the diagram described above. There is no question stem, options, or other accompanying text.