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DLS
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If two vertices of an equilateral triangle have integral coordinates,then the third vertex willl have
 one year ago
 one year ago
DLS Group Title
If two vertices of an equilateral triangle have integral coordinates,then the third vertex willl have
 one year ago
 one year ago

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DLS Group TitleBest ResponseYou've already chosen the best response.0
a)integral coordinates b)coordinates which are rational c)at least one coordinate irrational d)coordinates which are irrational
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
If a is an odd integer, b will not be an integer. dw:1356846803078:dw
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
dw:1356846856691:dw
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
Height of triangle c, is also the ycoordinate of the upper vertex. It's irrational.
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.0
how did u get a/2?
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
The triangle is equilateral, and all sides measure "a" long. The vertical height is the perpendicular bisector of the side that lies on the xaxis. Each half, therefore, measure a/2 long.
 one year ago

DLS Group TitleBest ResponseYou've already chosen the best response.0
can u possibly explain this?i got confused.. http://gyazo.com/077e2faa197346bf8450280343875ee2
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
Yes, I'll explain the whole thing. The problem states "two vertices of an equilateral triangle have integral coordinates" That means those coordinates are integers.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
To simplify the calculations, I set one vertex at (0, 0), and the orther one at (a, 0), with the condition that a is an integer.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
Because the triangle is equilateral, the third vertex lies in the perpendicular bisector of the first side which has coordinates (0, 0) and (a, 0).
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
The xcoordinate of the third vertex is the same as the xcoordinate of the midpoint of the first side. As such it's (x1 + x2)/2, but in our case, x1 is 0. So if x2, which is a, is odd, then the xcoordinate of the third vertex will not be an integer.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
So at least one coordinate may be not an integer. That rules out the first choice.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
That is b, the xcoordinate of the third vertex. b = a/2, and if a is odd, a/2 is not an integer.
 one year ago

mathstudent55 Group TitleBest ResponseYou've already chosen the best response.0
No, not yet. I was referring to small letter b in my drawing. The answer is C, you're right.
 one year ago
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