One endpoint of the line segment AB is A(5,-3). The midpoint of line segment AB is M(-1,-10). What are the coordinates of the other endpoint, B?
To find the coordinates of the other endpoint, B, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, M, between two endpoints, A(x1, y1) and B(x2, y2), can be found by taking the average of the x-coordinates and the average of the y-coordinates.
In this case, you have the coordinates of endpoint A (5, -3) and the midpoint M(-1, -10). Let's use the midpoint formula to find the coordinates of endpoint B.
The x-coordinate of midpoint M is (-1). The x-coordinate of endpoint A is 5. So, the x-coordinate of endpoint B can be found by taking the average of (-1) and 5:
(x1 + x2)/2 = (-1 + 5)/2 = 4/2 = 2
So, the x-coordinate of endpoint B is 2.
Similarly, the y-coordinate of midpoint M is (-10). The y-coordinate of endpoint A is (-3). So, the y-coordinate of endpoint B can be found by taking the average of (-10) and (-3):
(y1 + y2)/2 = (-10 + (-3))/2 = (-13)/2 = -6.5
So, the y-coordinate of endpoint B is -6.5.
Therefore, the coordinates of the other endpoint, B, are (2, -6.5).
Let the coordinates of point B be (x, y).
We can use the midpoint formula to solve for x and y:
x = (5 + x) / 2 ---> 2x = 5 + x ---> x = 5
y = (-3 + y) / 2 ---> 2y = -3 + y ---> y = -6
Therefore, the coordinates of point B are (5, -6).