The required other endpoint coordinates of line segment with one endpoint as (0,2) and a midpoint as (8,-9) is (16,-20).
Let there be line segment AB with mid- point M . We have been given the coordinates of one endpoint and midpoint which are,
A(0,2) and M(8,-9)
We have to find the coordinates of B of the line segment.
We know the formula of midpoint which is given as ,
(xm , ym) = [(x1 + x2)/2 , (y1 + y2)/2] (1)
Where (xm , ym) are the coordinates of the mid point which are (8,-9) and
(x1 , y1) = (0,2) are the coordinates of endpoint 1.
Thus we have to find (x2 , y2) coordinates. Putting the required value in equation (1) we get
(8 , -9) = [(0 + x2)/2 , (2 + y2)/2]
Therefore, 8 = x2/2 -9 = (2+y2)/2
x2 = 16 y2 = -20
Hence the required coordinates of the other endpoint is B(16,-20)
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