Coordiante Geometry

Question

 Each side of a square is 3 cm long. One vertex of the square is at (6,4) on the square coordinate grid marked in centimeter units. What are the possible combinations of another vertex of the square?

 

Please try to show all work! THANKS!!

Answer 1

Picture a square... Pick one corner to label as the point (6,4)

 

1.  If the bottom left vertex is at (6,4) then the bottom right is

a difference in the x coordinate of +3 so ((x+3),4) = (9,4)

The top left is 3 cm higher or (x,Y+3) = (6,7)

The top right is 3 cm higher than bottom right so (9,4+3) = (9,7)

 

Our vertices are  (6,4),(9,4),(6,7),(9,7)  if bottom left corner is at (6,4)

 

2.  If the bottom right corner is at (6,4) then the other vertices are

(6,4+3) = (6,7) for top right

(6-3,4) = (3,4) for bottom left

(3,4+3) = (3,7) for top left

 

So vertices would be (6,4),(6,7),(3,4),(3,7)

 

3.  If (6,4) is top left corner the other vertices are:

    (6,4-3) = (6,1)

    (6+3,1) = (9,1)

    (9,1+3) = (9,4)

 

4.  If (6,4) is top right the other vertices are

    (6,4-3) = (6,1)

    (6-3,1) = (3,1)

    (3,1+3) = (3,4)