Answer:
The coordinates of point S are (12, -18).
Explanation:
The midpoint formula is given by:
M = (x1 + x2) / 2, (y1 + y2) / 2, where
- M are the coordinates of the midpoint,
- (x1, y1) is one endpoint,
- and (x2, y2) is another endpoint.
We can find the x and y-coordinate of point S and then combine them at the end.
Finding the x-coordinate of point S:
We know that:
- the x-coordinate of point T is 0,
- and the x-coordinate of the midpoint ST is 6.
Now, we can find the x-coordinate of point S by substituting 0 for x1 and 6 for M in the midpoint formula:
(6 = (0 + x2) / 2) * 2
(12 = 0 + x2)
12 = x2
Thus, the x-coordinate of point S is 12.
Finding the y-coordinate of point S:
We also know that:
- the y-coordinate of point T is 2,
- and the y-coordinate of the midpoint ST is -8.
Now, we can find the y-coordinate of point S by substituting 2 for y1 and -8 for M in the midpoint formula:
(-8 = 2 + y2) / 2) * 2
(-16 = 2 + y2) - 2
-18 = y2
Thus, the y-coordinate of point S is -18.
Combining the coordinates of point S:
Therefore, the coordinates of point S are (12, -18).