Final answer:
You can find the other endpoint S of a line segment using the midpoint M and one endpoint R by setting up equations based on the midpoint formula and solving for the missing coordinates. In this case, the other endpoint S is found to have the coordinates (14, -4).
Step-by-step explanation:
To find the coordinates of the other endpoint S of a line segment when given the endpoint R and the midpoint M, we can use the midpoint formula. The midpoint formula states that the midpoint's coordinates are the average of the x-coordinates and the average of the y-coordinates of the endpoints. If we have one endpoint R(-6, 2) and the midpoint M(4, -1), we can set up two equations to find the coordinates of the other endpoint S(x, y):
- The average of the x-coordinates: (x - 6) / 2 = 4
- The average of the y-coordinates: (y + 2) / 2 = -1
Now we solve for x and y:
- x - 6 = 2(4)
- x = 8 + 6
- x = 14
- y + 2 = 2(-1)
- y = -2 - 2
- y = -4
The other endpoint S has the coordinates (14, -4).