SOLUTION: The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices. [ Ans: (1, 0), (1, 4) ] This question is from co-ordinate g

Algebra ->  Formulas -> SOLUTION: The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices. [ Ans: (1, 0), (1, 4) ] This question is from co-ordinate g      Log On


   

Question 1011804: The two opposite vertices of a square are (-1, 2) and (3, 2). Find the coordinates of other two vertices. [ Ans: (1, 0), (1, 4) ]
This question is from co-ordinate geometry.
I have got the first part of the answer (1,0) but can't get the other co-ordinate.
Please help me!
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonals of a square
bisect each other, and
are perpendicular to each other.
The two opposite vertices given are the ends of a horizontal diagonal on line y=2 .
The midpoint of that diagonal is M%28%28-1%2B3%29%2F2%2C2%29=M%281%2C2%29 .
That is also the midpoint of the other diagonal,
which is perpendicular to the horizontal diagonal,
meaning that it is on the vertical line x=1 .
The length of the horizontal half-diagonals is
1-%28-1%29=2 or 3-1=2 .
The length of the vertical half-diagonals must be the same,
so the two ends are 2 units above and below M ,
meaning at (1,2-2)=(1,0) and (1,2+2)=(1,4) .