Question 1171359
The midpoints of the sides of a triangle are (2,5),(4,2,(1,1).Find the coordinates of the three vertices.
<pre><b>
{{{drawing(400,400,-3,7,-3,7,

grid(1), triangle(2,5,4,2,1,1)  )}}}

In green, duplicate the left-most side below the right-most side
with one endpoint as that vertex:

{{{drawing(400,400,-3,7,-3,7,
green(line(3,-2,4,2)),
grid(1), triangle(2,5,4,2,1,1)  )}}}

In green, duplicate the left-most side again above the right-most side:

{{{drawing(400,400,-3,7,-3,7,
green(line(3,-2,4,2),line(4,2,5,6)),
grid(1), triangle(2,5,4,2,1,1)  )}}}

Connect the endpoints to the other two vertices

{{{drawing(400,400,-3,7,-3,7,
green(line(3,-2,4,2),line(4,2,5,6),line(5,6,2,5),line(3,-2,1,1)),
grid(1), triangle(2,5,4,2,1,1)  )}}}

Duplicate those last two lines at the vertices:

{{{drawing(400,400,-3,7,-3,7,
green(line(3,-2,4,2),line(4,2,5,6),line(5,6,2,5),line(3,-2,1,1),line(2,5,-1,4),line(-1,4,1,1)),
grid(1), triangle(2,5,4,2,1,1)  )}}}

What are the coordinates of those green vertices?

Edwin</pre></b>