The kitchen in Meghan’s house is a square. The points P(6, 2) and Q(0, 6) represent the opposite vertices of her kitchen in a drawing on a coordinate grid. Which of these ordered pairs could be a third vertex?

Question

zeesbrat3 · Answer

Answers:
 (0, 1)
 (1, 7)
 (5, 6)
 (5, 7)

mathteacher1729 · Answer

@zeesbrat3 do you have access to graphing paper?  The easiest way to do this is to literally plot the points. :)

zeesbrat3 · Answer

thanks for the idea! but if I didnt have graph paper, how would I do it? I do have graph paper, but I would like to know just in case

mathteacher1729 · Answer

My explanation of how to do this WITHOUT graph paper really relies on knowing what the picture WITH graph paper looks like, if that makes sense.

zeesbrat3 · Answer

it kind of makes sense, but when im graphing each of the coordinates, none of them make a square because, for it to be a square, all of the sides have to be equal

mathteacher1729 · Answer

I see how it could seem that way. But a square doesn't have to line up with the grid lines.

mathteacher1729 · Answer

Once you learn to think outside the grid lines, the inception sound goes off in your mind. :-p http://inception.davepedu.com/

ganeshie8 · Answer

im also not getting a square... imgetting 6 width, and 4 height

ganeshie8 · Answer

@mathteacher1729  opposite vertices means, diagonal vertices right ?

mathteacher1729 · Answer

Oh, yes. blargh. I assumed A and B are ADJACENT vertices. My fault. Still, there is a nice geometric view to this. One moment while I re-calibrate. :-p

ganeshie8 · Answer

waiting... i cant think of how its possible...

zeesbrat3 · Answer

Thank you! unless im missing something. I measured the distance, but none of them are equal. It says in the lesson that a square has all four sides that are equal. The rectangle is the one that has 2 sets of congruent sides, but not all sides are congruent.

ganeshie8 · Answer

@zeesbrat3  your concepts are perfect :)

question might be having a typo error... instead of "adjacent" , "opposite" would have come... :\

mathteacher1729 · Answer

Ok, here we go. 

A and B are the original points. They are opposite vertices of a square. 
The line joining A and B is one diagonal of the square. 
The line joining the OTHER diagonals must be of the same length. 
So find the perpendicular bisector of AB, then find the point on that line (the perp bisector of AB) which is equal distance from the center as A and B.

ganeshie8 · Answer

@mathteacher1729  amazing !!! i see it now :)))

zeesbrat3 · Answer

Me too! Thank you so much! That actually makes sense

mathteacher1729 · Answer

Woo, yay! Glad it helped. :)