anonymous
  • anonymous
Determine if triangle DEF with coordinates D (3, 2), E (4, 6), and F (7, 3) is an equilateral triangle. Use evidence to support your claim. If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific.
Geometry
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
I used the distance formula for each segment in triangle DEF and have come to the conclusion that the triangle is not an equilateral triangle. The distance for Segments DE and DF are sq.rt.17, but the distance for Segment EF is sq.rt. 18. I am having difficulty answering the second part of the question, "If it is not an equilateral triangle, what changes can be made to make it equilateral? Be specific." Please provide guidance as to how to go about answering this question. Thank you!
anonymous
  • anonymous
Find the distance between D and E to determine the length of Segment DE. D = (3,2) and E = (4,6) Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (4 - 3)^2 + (6 - 2)^2 Step 3: d = sq.rt. (1)^2 + (4)^2 Step 4: d = sq.rt. 1 + 16 Step 5: d = sq.rt. 17 Find the distance between E and F to determine the length of Segment EF. E = (4,6) and F = (7,3) Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (7 - 4)^2 + (3 - 6)^2 Step 3: d = sq.rt. (3)^2 + (-3)^2 Step 4: d = sq.rt. 9 + 9 Step 5: d = sq.rt. 18 Find the distance between D and F to determine the length of Segment DF. Step 1: d = sq.rt. (x2 - x1)^2 + (y2 - y1)^2 Step 2: d = sq.rt. (7 - 3)^2 + (3 - 2)^2 Step 3: d = sq.rt. (4)^2 + (1)^2 Step 4: d = sq.rt 16 + 1 Step 5: d = sq.rt. 17
DanJS
  • DanJS
i guess, sqrt(18) - sqrt(17) needs to be taken off EF, and recalculate the position of one of the points

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
I agree, but I have tried different combinations and have failed to find an alternative point.
Loser66
  • Loser66
By distance formula , you have \(EF =\sqrt{(7-4)^2+(3-6)^2}=\sqrt {18}\) Only one way you can do is to make it down to \(\sqrt{17}\)
anonymous
  • anonymous
That is what I thought before, but I got points off because I didn't give an alternative point.
Loser66
  • Loser66
by changing the location of E. F cannot be changed because it relates to D
Loser66
  • Loser66
if E( 6, 7) then you get the required triangle.
anonymous
  • anonymous
Seriously!?!
Loser66
  • Loser66
Read the problem, they say : by what changes??
anonymous
  • anonymous
Yes, thank you so much!
Loser66
  • Loser66
my change is the point E from (4, 6) to (6,7)
DanJS
  • DanJS
E or F can move in a circle around point D, right
Loser66
  • Loser66
@DanJS It is a good idea but I don't think they use the orbit concept here.
anonymous
  • anonymous
I plugged in 6,7 yet still got different measures for each distance. Did I do something wrong?
Loser66
  • Loser66
oh, yea!! I am wrong!!
Loser66
  • Loser66
since if you change E, then DE changes also. OMG. I am terribly sorry.
anonymous
  • anonymous
No worries!!
DanJS
  • DanJS
I dont see how that has to happen, if you move E , DE can stay the same length, the radius of the circle, when you move E on an Arc towards F
DanJS
  • DanJS
or F towards E the same way
anonymous
  • anonymous
Circle?
Loser66
  • Loser66
I know how to do!! Thanks God. He gives me a chance to fix my mistake. hehehe.
anonymous
  • anonymous
Lol thank you both for your help and patience!
DanJS
  • DanJS
Circle centered at D, radius root(17), you just swing F towards E or E towards F, till the chord EF is root17
DanJS
  • DanJS
i am guessing
DanJS
  • DanJS
or set up two distance formula , and use (x,y) for F, and figure out x and y, possibly
Loser66
  • Loser66
OK. \(DF=\sqrt{17}\)
anonymous
  • anonymous
I tried your second option, but every time I changed a coordinate, I failed to get the same measure for each segment.
Loser66
  • Loser66
\(DE=\sqrt{(x_E-3)^2+(y_E-2)^2)}\) \(EF=\sqrt{(7-x_E)^2+(3-y_E)^2)}\)
Loser66
  • Loser66
and we want DE = EF, so, solve for it!!
Loser66
  • Loser66
\(DE = EF = \sqrt{17}\)
DanJS
  • DanJS
that what i said.. :)
Loser66
  • Loser66
ok, take over, please. hehehe.. I tried to fix my mistake but if you know how to do, please, finish the stuff. I am not good at explaining. Please :)
anonymous
  • anonymous
So the change or different coordinate is (x,y)?
DanJS
  • DanJS
there are two possible points for F, one on each side of the Y axis, i think
DanJS
  • DanJS
17 = (x-4)^2 + (y-6)^2 17 = (x-3)^2 + (y-2)^2 i solved those with a computer,
anonymous
  • anonymous
So D still equals (3,2)...E still equals (4,6). What does F = ?
DanJS
  • DanJS
\[F(x,y) = (\frac{ 4\sqrt{3} + 7 }{ 2 } , \frac{ 8-\sqrt{3} }{ 2 }) \approx (6.9641, 3.1340)\]
anonymous
  • anonymous
Woah...that is very precise. I think I may have gone about answering this question the wrong way because I doubt my teacher would have expected such an answer.
anonymous
  • anonymous
Do you think I should answer using your original suggestion, "i guess, sqrt(18) - sqrt(17) needs to be taken off EF, and recalculate the position of one of the points,"....?
DanJS
  • DanJS
\[FD = FE = \sqrt{17}\] that what those 2 distance equations above are
anonymous
  • anonymous
Thank you for your help and time! If you could, would you please help me formulate my final answer. If not, I totally understand because I have already taken up so much of your time!!
DanJS
  • DanJS
draw a picture first
DanJS
  • DanJS
label everything
DanJS
  • DanJS
then maybe, move F up a little, and relable that F' point (x,y), EF' = root (17) to make an equilateral triangle
DanJS
  • DanJS
then use the work above
anonymous
  • anonymous
Okay, that is perfect! Thanks again. Can I give you multiple awards...other than just a medal?
anonymous
  • anonymous
*other not multiple
DanJS
  • DanJS
only things i know are fan and testimonial
anonymous
  • anonymous
Testimonial?
DanJS
  • DanJS
@Loser66 did just as much...
DanJS
  • DanJS
hover over name, and buttons are there
anonymous
  • anonymous
Okay, I gave you a medal, became a fan and submitted a testimonial. Thanks!!
DanJS
  • DanJS
hah, thanks, ill fan you to
anonymous
  • anonymous
No need!! Good night!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.