Find the other endpoint of a line segment with the given midpoint and one endpoint.
Endpoint: ( 6, -1); Midpoint:(15/2,2
To find the other endpoint of the line segment, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment can be found by taking the average of the x-coordinates and the average of the y-coordinates of the two endpoints.
Let's denote the coordinates of the other endpoint as (x, y).
Given that one endpoint is (6, -1) and the midpoint is (15/2, 2), we can set up the following equations:
(6 + x) / 2 = 15/2 [Equation 1]
(-1 + y) / 2 = 2 [Equation 2]
Now, let's solve for x and y:
[Equation 1]:
Multiply both sides by 2:
6 + x = 15
Subtract 6 from both sides:
x = 9
[Equation 2]:
Multiply both sides by 2:
-1 + y = 4
Subtract -1 from both sides:
y = 5
Therefore, the other endpoint of the line segment is (9, 5).