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 2 years ago
If two vertices of an equilateral triangle have integral coordinates,then the third vertex willl have
 2 years ago
If two vertices of an equilateral triangle have integral coordinates,then the third vertex willl have

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

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0If a is an odd integer, b will not be an integer. dw:1356846803078:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1356846856691:dw

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0Height of triangle c, is also the ycoordinate of the upper vertex. It's irrational.

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

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

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

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0To 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.

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

mathstudent55
 2 years ago
Best ResponseYou've already chosen the best response.0The 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.

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

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

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