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

1. DLS

a)integral co-ordinates b)co-ordinates which are rational c)at least one co-ordinate irrational d)co-ordinates which are irrational

2. DLS

@LogicalApple

3. mathstudent55

If a is an odd integer, b will not be an integer. |dw:1356846803078:dw|

4. mathstudent55

|dw:1356846856691:dw|

5. mathstudent55

Height of triangle c, is also the y-coordinate of the upper vertex. It's irrational.

6. DLS

how did u get a/2?

7. 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.

8. DLS

can u possibly explain this?i got confused.. http://gyazo.com/077e2faa197346bf8450280343875ee2

9. 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.

10. 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.

11. DLS

okay

12. 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).

13. DLS

yes

14. 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.

15. DLS

yes..

16. mathstudent55

So at least one coordinate may be not an integer. That rules out the first choice.

17. DLS

is it C?

18. 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.

19. DLS

20. mathstudent55

No, not yet. I was referring to small letter b in my drawing. The answer is C, you're right.

21. DLS

yes,thanks!