Final answer:
The coordinates of point B are (14,9), determined by using the midpoint formula to calculate the average of the x-coordinates and y-coordinates between points A and B.
Step-by-step explanation:
To find the coordinates of point B when given the midpoint M of a line segment AB and one endpoint A, we use the midpoint formula which states that the midpoint M is the average of the x-coordinates and the y-coordinates of the endpoints A and B.
Given M(12,7) and A(10,5), we can set up two equations:
- The average of the x-coordinates: (xA + xB)/2 = xM
- The average of the y-coordinates: (yA + yB)/2 = yM
Plugging in the given values, we have:
- (10 + xB)/2 = 12
- (5 + yB)/2 = 7
Solving for xB and yB, we find:
- 10 + xB = 24 → xB = 14
- 5 + yB = 14 → yB = 9
Therefore, the coordinates of point B are (14, 9).