Final answer:
To find the coordinates of points A and B given the midpoint M and the length MB, we use the fact that A and B are equidistant from M along the number line. By adding and subtracting the length MB from M's coordinate, we determine two possible coordinates for A and B.
Step-by-step explanation:
The question involves finding the coordinates of points A and B given the coordinates of the midpoint M and the length of the segment MB. This problem requires an understanding of the midpoint formula in a one-dimensional coordinate system. Since the midpoint M is the average of the coordinates of A and B, and we have the distance from M to B, we can calculate the positions of A and B on the number line.
For number 18, with midpoint m = 7 and MB = 9, we have two possible solutions for B: B could be at 7 + 9 = 16 or at 7 - 9 = -2. Since M is the midpoint, A must be equidistant from M on the opposite side as B. Thus, if B is at 16, then A is at 7 - 9 = -2, and if B is at -2, then A is at 7 + 9 = 16.
For number 19, with midpoint m = -6 and MB = 3, we have two possible solutions for B: B could be at -6 + 3 = -3 or at -6 - 3 = -9. Therefore, if B is at -3, then A is at -6 - 3 = -9, and if B is at -9, then A is at -6 + 3 = -3.