Final answer:
The coordinates of point C are calculated using the midpoint formula. Given the midpoint A (-1, 0) and endpoint T (1, 2), point C is found to be (-3, -2), which is option D.
Step-by-step explanation:
The question asks to find the coordinates of point C if point A is the midpoint of segment CT, with given coordinates for points A and T. The midpoint formula states that the midpoint M is calculated using the coordinates of endpoints C(x1, y1) and T(x2, y2) as M((x1 + x2)/2, (y1 + y2)/2). Since A is the midpoint, we have the midpoint's coordinates as (-1, 0) and T's coordinates as (1, 2).
Let's find the coordinates of C by setting up the equations based on the midpoint formula:
- For the x-coordinate: (-1 + 1)/2 = x1/2 ⇒ -1 + 1 = x1 ⇒ x1 = -3
- For the y-coordinate: (0 + 2)/2 = y1/2 ⇒ 0 + 2 = y1 ⇒ y1 = -2
Thus, the coordinates of point C are (-3, -2), which corresponds to option D.