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.

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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.

Mathematics
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@jim_thompson5910 @geekfromthefutur can u please help me ??
You need to prove that DE = EF = DF
To find the length of DE, you find the distance from D to E Use the distance formula \[\Large d = \sqrt{\left(x_{2}-x_{1}\right)^2+\left(y_{2}-y_{1}\right)^2}\]

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oh ok give me one second (:
Alright, take all the time you need. I'll be right back
ok (:
@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?
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
I think you meant to use D,E,F instead of A,B,C ?
yea sorry (:
You should have \[ DE = \sqrt{17}\\ EF = \sqrt{18}\\ DF = \sqrt{17}\\ \] So it looks like you got it
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
oh ok i see what mean (: thank you so much (:
you're welcome
@jim_thompson5910 could help me with another Question if u have the chance??
sure, just post where it says 'ask a question' so you have more room and less clutter
oh ok (: thank you
np

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