One endpoint of a line segment is (-7, 2). The midpoint of the line segment is (-1, -2). What are the co-ordinates of the other endpoint?
I don't want the answer just a formula
the other endpoint is just as far from the midpoint as the first end is. So, If you have points A,M,B, then
B = M + (M-A)
That is,
Bx = Mx + (Mx-Ax)
By = My + (My-Ay)
Or, as you can see, B = 2M-A
If (a,b) and (c,d) are any two points, then the midpoint is ((a+c)/2 , (b+d)/2) )
Thanks Steve:)
To find the coordinates of the other endpoint of the line segment, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
In this case, we are given that one endpoint is (-7, 2) and the midpoint is (-1, -2). We can let the coordinates of the other endpoint be (x, y).
Using the midpoint formula, we can set up the following equations:
-1 = (-7 + x) / 2 (x-coordinate of the midpoint)
-2 = (2 + y) / 2 (y-coordinate of the midpoint)
To solve for x, we multiply both sides of the first equation by 2:
-2 = -7 + x
Adding 7 to both sides:
5 = x
So the x-coordinate of the other endpoint is 5.
Similarly, to solve for y, we multiply both sides of the second equation by 2:
-4 = 2 + y
Subtracting 2 from both sides:
-6 = y
So the y-coordinate of the other endpoint is -6.
Therefore, the coordinates of the other endpoint are (5, -6).