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

- anonymous

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

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- anonymous

- anonymous

A) (-2,4)
B) (-2,3)
C) (-3,3)
D) (-3,4)

- anonymous

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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## More answers

- anonymous

anone wanna assist me please? i wanna learn how to do this myself :(

- anonymous

@ParthKohli @pooja195 @Data_LG2

- anonymous

@hartnn @nincompoop @Abhisar

- anonymous

@misty1212

- baru

that formula you have typed out, do you know what it's for?

- anonymous

@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

- baru

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

- baru

if you say triangle ABC congruent to DEF
it means
AB=DE
BC=EF
AC=DF

- baru

with me so far?

- anonymous

yes :)

- anonymous

so how would i calculate f using the formula? would i use the distance between BC or Ac to find F or?...

- baru

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

- anonymous

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 :(

- baru

yeah, exactly

- baru

find the lengths EF and DF for each of the options, compare with the lengths AC and BC

- anonymous

but how will i know it is right?

- anonymous

@baru

- anonymous

oh wait i THINK i understand, if they have the same result as the sides of the congruent triangle thats already there (abs) ?

- anonymous

*c

- baru

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)

- anonymous

so i go all around? ok so first i find EF=AC right?

- baru

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

- anonymous

ok let me find AC and BC first

- anonymous

@baru can you help me place the points into the formula?
A = (1,-1)
C= (2,3)
B= (-1,2)
C= (2,3)

- baru

\[AC = \sqrt{(1-2)^2 + (-1-3)^2}\]

- baru

\[BC = \sqrt{(-1-2)^2 + (2-3)^2}\]

- anonymous

@baru but how did you place them?
like which value was x1 x2 and y1 y2 ?

- baru

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

- baru

umm... how did you get A=(1,-1) ??

- anonymous

i looked at the graph to see where the point is, did i saw it wrong? omg let me see haha

- anonymous

is it (1,0)?

- baru

yep :)

- baru

so if you want to find the length AC
then think of A =(x1,y1) and C=(x2,y2)

- baru

so, x1=1 and y1=0
x2=2 and y2=3

- anonymous

ohhhhhh kk hha now ill find AC

- anonymous

i got 10 for AC

- anonymous

AM I RIGHT? @baru

- anonymous

lol i wanna make sure

- anonymous

i have a feeling i am doing it wrong

- anonymous

or is everything supoosed to stay in the sqr root ?

- anonymous

so its supposed to be the sqr root of 10?

- anonymous

so2 is my answer?

- baru

yep, AC is square root of 10.

- anonymous

so then i find BC?

- baru

not necessary, option 2 is the only one which gives you EF= square root of 10

- baru

did you try finding EF for all the options?

- anonymous

what do you mean?

- baru

i'm sorry i meant DF

- baru

we established that for the two triangles to be congruent,
length AC = length DF

- baru

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

- anonymous

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?

- baru

what do you mean "so i can test B' ?

- anonymous

option b for F

- baru

oh..lol. Yep, you are absolutely right then

- anonymous

yay! lol

- anonymous

kk ima test it

- baru

alright

- anonymous

@baru i got the square root of ten aswell!~ does this mean B is my answer? :)

- baru

yup

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