## anonymous one year ago Determine if triangle DEF with coordinates D(2, 1), E(3, 5), and F(6, 2) is an equilateral triangle. Use evidence to support your claim.

1. anonymous

2. jim_thompson5910

You need to prove that DE = EF = DF

3. jim_thompson5910

To find the length of DE, you find the distance from D to E Use the distance formula $\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}$

4. jim_thompson5910

|dw:1434592177602:dw|

5. anonymous

oh ok give me one second (:

6. jim_thompson5910

Alright, take all the time you need. I'll be right back

7. anonymous

ok (:

8. anonymous

@jim_thompson5910 sorry to bother but im stuck on a part its the coordinates (6,2) im not sure where it would go but i know (2,1) would plug into (x1,x2) and then coordinates (3,5) would plug into (y1,y2) right?

9. jim_thompson5910

D(2, 1), E(3, 5), let D be the point (x1,y1) let E be the point (x2,y2) so x1 = 2 x2 = 3 y1 = 1 y2 = 5 $\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}$ $\Large d = \sqrt{\left(3-2\right)^2+\left(5-1\right)^2}$ $\Large d = \sqrt{\left(1\right)^2+\left(4\right)^2}$ $\Large d = \sqrt{1+16}$ $\Large d = \sqrt{17}$ So DE is exactly $$\Large \sqrt{17}$$ units long. I'll let you do the other segments EF and DF

10. jim_thompson5910

I think you meant to use D,E,F instead of A,B,C ?

11. anonymous

yea sorry (:

12. jim_thompson5910

You should have $DE = \sqrt{17}\\ EF = \sqrt{18}\\ DF = \sqrt{17}\\$ So it looks like you got it

13. jim_thompson5910

DE = DF is true but DE = EF is false so not all sides are equal to the same length we don't have an equilateral triangle, but we do have an isosceles triangle

14. anonymous

oh ok i see what mean (: thank you so much (:

15. jim_thompson5910

you're welcome

16. anonymous

@jim_thompson5910 could help me with another Question if u have the chance??

17. jim_thompson5910

sure, just post where it says 'ask a question' so you have more room and less clutter

18. anonymous

oh ok (: thank you

19. jim_thompson5910

np