Find the other endpoint of the line segment with the given endpoint and mid point.
1. Endpoint:(-1, 9), midpoint: (-9, -10)
2. Endpoint: (2, 5), midpoint: (5, 1)
3. Endpoint:(9, -10), midpoint: (4, 8)
I will do the 2nd
You do the others the same way....
Let the other endpoint be (x,y)
(x+2)/2 = 5 and (y+5)/2 = 1
x+2 = 10 and y+5 = 2
x = 8 and y = -3
the other endpoint is (8,-3)
To find the other endpoint of a line segment given one endpoint and the midpoint, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment are equal to the average of the coordinates of the two endpoints.
Let's use this formula to find the other endpoint for each given situation:
1. Endpoint: (-1, 9), midpoint: (-9, -10)
To find the other endpoint, we need to find the difference between the x-coordinates and y-coordinates of the given endpoint and the midpoint, and then subtract or add those differences to the coordinates of the midpoint.
x-coordinate difference = (-1) - (-9) = 8
y-coordinate difference = 9 - (-10) = 19
To find the other endpoint, we add the differences to the coordinates of the midpoint:
x-coordinate of the other endpoint = -9 + 8 = -1
y-coordinate of the other endpoint = -10 + 19 = 9
Therefore, the other endpoint is (-1, 9).
2. Endpoint: (2, 5), midpoint: (5, 1)
Following the same steps as above:
x-coordinate difference = 2 - 5 = -3
y-coordinate difference = 5 - 1 = 4
x-coordinate of the other endpoint = 5 + (-3) = 2
y-coordinate of the other endpoint = 1 + 4 = 5
Therefore, the other endpoint is (2, 5).
3. Endpoint: (9, -10), midpoint: (4, 8)
Once again, applying the same steps:
x-coordinate difference = 9 - 4 = 5
y-coordinate difference = -10 - 8 = -18
x-coordinate of the other endpoint = 4 + 5 = 9
y-coordinate of the other endpoint = 8 + (-18) = -10
Therefore, the other endpoint is (9, -10).