Final answer:
The coordinates of point C are found using the midpoint formula, resulting in C having coordinates (2, 12), where B is the midpoint of segment AC.
Step-by-step explanation:
To find the coordinates of point C, given that B is the midpoint of segment AC, and you have the coordinates of A (12,6) and B (7,9), you can use the midpoint formula. The midpoint formula is (Ax + Cx) / 2 = Bx and (Ay + Cy) / 2 = By, where (Ax, Ay) are the coordinates of A, (Bx, By) are the coordinates of B, and (Cx, Cy) are the coordinates of C. Since B is the midpoint, we can rearrange the formulas to solve for Cx and Cy.
Calculating Cx: (12 + Cx) / 2 = 7, so 12 + Cx = 14, which means Cx = 14 - 12, so Cx = 2.
Calculating Cy: (6 + Cy) / 2 = 9, so 6 + Cy = 18, so Cy = 18 - 6, so Cy = 12.
Therefore, the coordinates of C are (2, 12).