Question

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.

Answer 1

@jim_thompson5910 @geekfromthefutur can u please help me ??

Answer 2

You need to prove that

DE = EF = DF

Answer 3

To find the length of DE, you find the distance from D to E

Use the distance formula

\[\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]

Answer 4

oh ok give me one second (:

Answer 5

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

Answer 6

ok (:

Answer 7

@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?

Answer 8

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

Answer 9

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

Answer 10

yea sorry (:

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

you're welcome

Answer 15

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

Answer 16

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

Answer 17

oh ok (: thank you

Answer 18

np