# Thread: Determining the vertices and its area

1. ## Determining the vertices and its area

a square whose vertices coincide with the endpoints of the line from (1,3) to (3,-1). determine the other vertices and its area.

2. ## Re: Determining the vertices and its area

Originally Posted by dwightlumanta321
a square whose vertices coincide with the endpoints of the line from (1,3) to (3,-1). determine the other vertices and its area.
You have one of the diagonals of your square, can you get its equation?
Can you find its midpoint of this line segment and use this and the line to evaluate the equation of the other diagonal of your square?

3. ## Re: Determining the vertices and its area

what does "coincide" means?

4. ## Re: Determining the vertices and its area

Originally Posted by dwightlumanta321
what does "coincide" means?
While I am not 100% sure, I took it to mean that the vertices given were opposite corners.

5. ## Re: Determining the vertices and its area

Hello, dwightlumanta321!

We have a square. .Two of its vertices are (1,3) and (3,-1).
Determine the other vertices and its area.

The problem is not clearly stated.

If the two vertices are consecutive vertices,
. . there are two scenarios. .This is one of them.
Code:
      |         +4    D
|   + - - - - - o (5,5)
|   :        *
| +2:     *       *
|     -*
| A o {1,3)         *
|   :
|   : *               *
|   :                       C
| -4:   *               o (7,1)
|   :                *  :
----+---:-----*-------*-----: -2 ----
|   :          *        :
|   + - - - o - - - - - +
|     +2  (3,-1)   +4
|           B
Going from $A$ to $B$, we move right 2, down 4.
Hence, going from $B$ to $C$, we move right 4, up 2.
And going from $A$ to $D$, we move right 4, up 2.

If those are opposite vertices, we have this diagram.
Code:
      |
|   A
| (1,3)
|   o - +
|    \  :       D
|     \ :       o (4,2}
|      \:M      :
+ - - - o - - - +
B:   (2,1)\
----o---------\----------
|(0,0)     \
|           o
|         (3,-1)
|           C
To go from $A(1,3)$ to $M(2,1)$ (the midpoint of $AC$),
. . we go 1 right, down 2.

Hence, to go from $M$ to $B$, we go left 2, down 1.
And to go from $M$ to $D$. we go right 2, up 1.