DLS
  • DLS
If two vertices of an equilateral triangle have integral coordinates,then the third vertex willl have
Mathematics
chestercat
  • chestercat
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DLS
  • DLS
a)integral co-ordinates b)co-ordinates which are rational c)at least one co-ordinate irrational d)co-ordinates which are irrational
DLS
  • DLS
@LogicalApple
mathstudent55
  • mathstudent55
If a is an odd integer, b will not be an integer. |dw:1356846803078:dw|

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mathstudent55
  • mathstudent55
|dw:1356846856691:dw|
mathstudent55
  • mathstudent55
Height of triangle c, is also the y-coordinate of the upper vertex. It's irrational.
DLS
  • DLS
how did u get a/2?
mathstudent55
  • mathstudent55
The triangle is equilateral, and all sides measure "a" long. The vertical height is the perpendicular bisector of the side that lies on the x-axis. Each half, therefore, measure a/2 long.
DLS
  • DLS
can u possibly explain this?i got confused.. http://gyazo.com/077e2faa197346bf8450280343875ee2
mathstudent55
  • mathstudent55
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.
mathstudent55
  • mathstudent55
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.
DLS
  • DLS
okay
mathstudent55
  • mathstudent55
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).
DLS
  • DLS
yes
mathstudent55
  • mathstudent55
The x-coordinate of the third vertex is the same as the x-coordinate 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 x-coordinate of the third vertex will not be an integer.
DLS
  • DLS
yes..
mathstudent55
  • mathstudent55
So at least one coordinate may be not an integer. That rules out the first choice.
DLS
  • DLS
is it C?
mathstudent55
  • mathstudent55
That is b, the x-coordinate of the third vertex. b = a/2, and if a is odd, a/2 is not an integer.
DLS
  • DLS
answer=b?
mathstudent55
  • mathstudent55
No, not yet. I was referring to small letter b in my drawing. The answer is C, you're right.
DLS
  • DLS
yes,thanks!

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