Final answer:
The coordinates of the point where the diagonals of the parallelogram formed by joining the given points meet are (1,1). This is found by averaging the x-coordinates and y-coordinates of opposite corners of the parallelogram.
Step-by-step explanation:
The question involves finding the coordinates of the point where the diagonals of the parallelogram meet. A parallelogram's diagonals bisect each other, meaning that the midpoint of one diagonal is also the midpoint of the other diagonal. Given the four vertices of the parallelogram (−2,−1), (1,0), (4,3), and (1,2), the midpoint can be found by averaging the x-coordinates and the y-coordinates of any two opposite corners. For example, using the points (−2,−1) and (4,3), we calculate the midpoint (meeting point of the diagonals) as follows:
- M_x = (x_1 + x_2) / 2 = (−2 + 4) / 2 = 1
- M_y = (y_1 + y_2) / 2 = (−1 + 3) / 2 = 1
Therefore, the coordinates of the point where the diagonals of the parallelogram meet are (1,1).