Final answer:
The midpoint formula was used to find the coordinates of point C given P and midpoint O, resulting in coordinates (-3, 0), which do not match the given options, suggesting there might be an error in the question's statement. Therefore, the coordinates of C are (-3, 0), which is not listed in the options provided
Step-by-step explanation:
The midpoint formula was used to find the coordinates of point C given P and midpoint O, resulting in coordinates (-3, 0), which do not match the given options, suggesting there might be an error in the question's statement. The student is asking for the coordinates of point C given that zero is the midpoint of segment PC, with known coordinates for points P (11, 12) and O (4, 6).
To find the coordinates of C, we need to use the midpoint formula which states that the midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) has coordinates M = ((x1 + x2)/2, (y1 + y2)/2). Since O is the midpoint of PC, we can set up the equations (11 + x)/2 = 4 and (12 + y)/2 = 6.
Solving for x and y gives us x = -3 and y = 0. Therefore, the coordinates of C are (-3, 0), which is not listed in the options provided, indicating a possible typo in the question or that the question statement might have an error in referring to point 'O' as the midpoint, instead of 'zero' which may imply the origin (0, 0).