Question

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

Answer 1

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

Answer 2

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.

\[\sqrt{(y1-y2)^2+ (x1-x2)^2}\]

Answer 3

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

Answer 4

@ParthKohli @pooja195 @Data_LG2

Answer 5

@hartnn @nincompoop @Abhisar

Answer 6

@misty1212

Answer 7

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

Answer 8

@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

Answer 9

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

Answer 10

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

Answer 11

with me so far?

Answer 12

yes :)

Answer 13

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

Answer 14

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

Answer 15

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 :(

Answer 16

yeah, exactly

Answer 17

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

Answer 18

but how will i know it is right?

Answer 19

@baru

Answer 20

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

Answer 21

*c

Answer 22

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)

Answer 23

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

Answer 24

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

Answer 25

ok let me find AC and BC first

Answer 26

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

B= (-1,2)
C= (2,3)

Answer 27

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

Answer 28

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

Answer 29

@baru but how did you place them?

like which value was x1 x2 and y1 y2 ?

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

is it (1,0)?

Answer 34

yep :)

Answer 35

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

Answer 36

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

Answer 37

ohhhhhh kk hha now ill find AC

Answer 38

i got 10 for AC

Answer 39

AM I RIGHT? @baru

Answer 40

lol i wanna make sure

Answer 41

i have a feeling i am doing it wrong

Answer 42

or is everything supoosed to stay in the sqr root ?

Answer 43

so its supposed to be the sqr root of 10?

Answer 44

so2 is my answer?

Answer 45

yep, AC is square root of 10.

Answer 46

so then i find BC?

Answer 47

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

Answer 48

did you try finding EF for all the options?

Answer 49

what do you mean?

Answer 50

i'm sorry i meant DF

Answer 51

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

Answer 52

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

Answer 53

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?

Answer 54

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

Answer 55

option b for F

Answer 56

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

Answer 57

yay! lol

Answer 58

kk ima test it

Answer 59

alright

Answer 60

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

Answer 61

yup