Find the other endpoint of the line segments with the given endpoint and midpoint.
Endpoint: (-5,4)
Midpoint: (-10,-6)
What is the endpoint for the endpoint and midpoint above.
Let the coordinates of the other endpoint be (x,y).
Using the midpoint formula, we know that the midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints. Therefore, we have:
(x + (-5))/2 = -10/2 ---> (x - 5)/2 = -5
(x - 5) = -5*2 ---> x - 5 = -10
x = -10 + 5 ---> x = -5
Similarly, we have:
(y + 4)/2 = -6/2 ---> (y + 4)/2 = -3
(y + 4) = -3*2 ---> y + 4 = -6
y = -6 - 4 ---> y = -10
Therefore, the other endpoint is (-5, -10).
To find the other endpoint of the line segment, we can use the midpoint formula. The midpoint formula states that the midpoint between two endpoints (x1, y1) and (x2, y2) is given by the coordinates:
(x1 + x2) / 2, (y1 + y2) / 2
Given that the endpoint is (-5, 4) and the midpoint is (-10, -6), we can write the following equation using the midpoint formula:
(-5 + x2) / 2 = -10
(4 + y2) / 2 = -6
To solve for x2, we can multiply both sides of the first equation by 2:
-5 + x2 = -20
Then, adding 5 to both sides, we have:
x2 = -20 + 5 = -15
To solve for y2, we can multiply both sides of the second equation by 2:
4 + y2 = -12
Then, subtracting 4 from both sides, we have:
y2 = -12 - 4 = -16
Therefore, the other endpoint of the line segment is (-15, -16).