What coordinate for F would make triangle ABC and triangle DEF congruent?

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What coordinate for F would make triangle ABC and triangle DEF congruent?

Mathematics
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A) (-2,4) B) (-2,3) C) (-3,3) D) (-3,4)
i believe that the answer is B , but that is just because i looked at the graph. its like an overlapping reflection, correct? i need help, i need someone to walk me through this . is there like, a formula? the lesson shows me this formula but its not clear on how to use it. \[\sqrt{(y1-y2)^2+ (x1-x2)^2}\]

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anone wanna assist me please? i wanna learn how to do this myself :(
that formula you have typed out, do you know what it's for?
@baru i THINK its to find the distance between two points, the lesson doesnt get detailed in it though :( they just start using it through examples
you are right, its for the distance between two points. for two triangles to be congruent, the sides of the triangles should have equal lengths
if you say triangle ABC congruent to DEF it means AB=DE BC=EF AC=DF
with me so far?
yes :)
so how would i calculate f using the formula? would i use the distance between BC or Ac to find F or?...
yeah..that would be the right way, but rather than solve for the co-ordinates of F, you are given several options for F, just substitute them and find EF and DF, see which one is equal to BC,AC
so i use my options for F? and place them in the formula? im sorry if i dont quite understand, im a slow thinker in the morning :(
yeah, exactly
find the lengths EF and DF for each of the options, compare with the lengths AC and BC
but how will i know it is right?
oh wait i THINK i understand, if they have the same result as the sides of the congruent triangle thats already there (abs) ?
*c
you have to do it for each option. only one option will give you EF=AC and DF=BC (you have to find lengths AC and BC as well)
so i go all around? ok so first i find EF=AC right?
first calculate AC and BC and write it down. then find EF for each option, see which one matches the value for AC that you just wrote down
ok let me find AC and BC first
@baru can you help me place the points into the formula? A = (1,-1) C= (2,3) B= (-1,2) C= (2,3)
\[AC = \sqrt{(1-2)^2 + (-1-3)^2}\]
\[BC = \sqrt{(-1-2)^2 + (2-3)^2}\]
@baru but how did you place them? like which value was x1 x2 and y1 y2 ?
oh...ok. wait. neglect what i typed just above, i have reversed the formula you gave(but it doesn't really matter). ill type it in detail, wait
umm... how did you get A=(1,-1) ??
i looked at the graph to see where the point is, did i saw it wrong? omg let me see haha
is it (1,0)?
yep :)
so if you want to find the length AC then think of A =(x1,y1) and C=(x2,y2)
so, x1=1 and y1=0 x2=2 and y2=3
ohhhhhh kk hha now ill find AC
i got 10 for AC
AM I RIGHT? @baru
lol i wanna make sure
i have a feeling i am doing it wrong
or is everything supoosed to stay in the sqr root ?
so its supposed to be the sqr root of 10?
so2 is my answer?
yep, AC is square root of 10.
so then i find BC?
not necessary, option 2 is the only one which gives you EF= square root of 10
did you try finding EF for all the options?
what do you mean?
i'm sorry i meant DF
we established that for the two triangles to be congruent, length AC = length DF
you have found that the length AC is square root of ten. the question gives you several options for the co-ordinates of F. so find the length DF for each of the options, and see which one gives you square root of 10
ohhhhhhhhhhhhhhhhhhhhhh ok ok ok so i can test B and see if it gives me squeare rot of 10? and if it does it means that my answer is correct? but if it isnt i keep testing the other options until it matches square root of 10?
what do you mean "so i can test B' ?
option b for F
oh..lol. Yep, you are absolutely right then
yay! lol
kk ima test it
alright
@baru i got the square root of ten aswell!~ does this mean B is my answer? :)
yup

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