Final answer:
The coordinates for point B, when C (12, 3) is the midpoint of segment AB and A is at (7, 2), are (17, 4) by using the midpoint formula to find B's X and Y values.
Step-by-step explanation:
To find the coordinates for point B when point C is the midpoint of segment AB and A is known, we use the midpoint formula. The midpoint C has coordinates (12, 3), and point A has coordinates (7, 2). The midpoint formula says that the coordinates of the midpoint are the averages of the X and Y coordinates of the endpoints:
Mₓ = (Aₓ + Bₓ ) / 2 and Mᵧ = (Aᵧ+ Bᵧ) / 2.
Substituting the known values, we have:
12 = (7 + Bₓ ) / 2 and 3 = (2 + Bᵧ) / 2.
By solving these equations, we find:
- Bₓ = 2 * 12 - 7
- Bᵧ = 2 * 3 - 2
Thus, Bₓ = 17 and Bᵧ = 4, so the coordinates for point B are (17, 4).