Final answer:
The coordinates of point P, when O is at the origin and (-1,2) is the midpoint, are (-2,4).
Step-by-step explanation:
If the midpoint of the line segment OP is given as (-1,2) and point O is the origin (0,0), you can find the coordinates of the point P by using the midpoint formula. The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by M = ((x1 + x2)/2, (y1 + y2)/2). Since we know that M (-1,2) and one endpoint O (0,0), we can set up the following equations to solve for the coordinates of P (x2, y2):
- (0 + x2)/2 = -1 → x2 = -2
- (0 + y2)/2 = 2 → y2 = 4
Therefore, the coordinates of point P are (-2, 4).