Since, the coordinates of the midpoint of line RS are M[tex](3, 5)[/tex].
The coordinates of endpoint R are (-2,10)
We have to determine the coordinates of endpoint S.
The midpoint of the line segment joining the points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by the formula [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].
Here, The endpoint R is (-2,10) So, [tex]x_1 = -2 , y_1=10[/tex]
Let the endpoint S be [tex](x_2,y_2)[/tex]
The midpoint coordinate M is [tex](3, 5)[/tex].
So, [tex]3 = \frac{-2+x_2}{2}[/tex]
[tex]{6} = {-2+x_2}[/tex]
[tex]{x_2}=8[/tex]
Now, [tex]5 = \frac{10+y_2}{2}[/tex]
[tex]10 = {10+y_2}[/tex]
[tex]0= y_2[/tex]
So, the other endpoint S is (8,0).
