Question

DESPERATE GEOMETRY HELP
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. If it is not an equilateral triangle, what changed could be made to make it equilateral?

Answer 1

guess we gotta use the distance formula a few times to see if the distances are the same

Answer 2

okay

Answer 3

first a nice picture
http://www.wolframalpha.com/input/?i=triangle+%282%2C1%29%2C+%283%2C5%29%2C++%286%2C2%29+

Answer 4

as you can see it is an isosceles acute triangle not equilateral

Answer 5

the distance between \((2,1)\) and \((3,5)\) is \[\sqrt{(3-2)^2+(5-1)^2}=\sqrt{1+16}=\sqrt{17}\]

Answer 6

the distance between \((2,1)\) and \((6,2)\) is also \(\sqrt{17}\) the computation is almost identical

Answer 7

but the distance between \((3,5)\) and \((6,2)\) is
\[\sqrt{(6-3)^26(5-2)^2}=\sqrt{3^2+3^2}=3\sqrt2\]

Answer 8

wouldnt you do 3 squared nd 3 squared and add thos and THEN square root it?

Answer 9

hello??

Answer 10

yes
lets check and make sure it is clear you get the same thing i wrote since i guess i skipped a step

Answer 11

\[\sqrt{3^2+3^2}=\sqrt{9+98}=\sqrt{18}=\sqrt{9\times 2}=3\sqrt2\]

Answer 12

damn typo
second one should be \(\sqrt{9+9}\)

Answer 13

okiiee

Answer 14

so how would you make it equilateral?

Answer 15

hmm lets go back to the picture
i guess we have to adjust one of the points

Answer 16

okay

Answer 17

lol actually i have no idea
let me think about it for a moment, it is kind of a weird question

Answer 18

ok

Answer 19

lol i can't think of what to do
repost the second part, maybe someone has a good idea