We have the following:
A(-5, 1)
M(1, 4)
B(x1, y1)
In order to first determine the point B, we do the following:
we first determine the lenght from the point A to the midpoint M:
[tex](1,\text{ 4)}-(-5,1)\Rightarrow(6,\text{ }3)[/tex][tex]D_{AM}=\sqrt[]{(6)^2+(3)^2}^{}\Rightarrow D_{AM}=3\sqrt[]{5}[/tex]From this, we do as follows:
*Fisrt we determine the form of the distance to that other point using our mid point or our start point A:
[tex](x,y)-(1,4)=(x-1,y-4)[/tex]Or
[tex](x,y)-(-5,1)=(x+5,y-1)[/tex]Where in our first case The distance should be 3sqrt(5).
From this, we can calculate that the point (7, 7) will be our B point. That can be seen as follows:
[tex](7-1,7-4)=(6,3)[/tex]Since the vector that is formed from the vector B to the midpoint is the same as the vector formed from the midpoint to A.
And the distance of both is double the distance from A to M.
