Question

Which series of transformations on figure 1 can be used to show that the figures are congruent ?

Answer 1

What is figure 1?

Answer 2

@Vocaloid

Answer 3

if this is like a graded test I'm not sure I can answer this and abide by the rules of the site

Answer 4

oh no it's look like that

Answer 5

that's how our assignments look like that

Answer 6

crop image

Answer 7

i can't that's only picture i have

Answer 8

well in any case you would just go through the answer choices one by one and see which transformation produces the image

Answer 9

B.

Answer 10

that's a good guess but a clockwise rotation would make the image look like this

Answer 11

thoughts on C or D?

Answer 12

C cause it's makes sense coming from your example

Answer 13

good, C

Answer 14

i think the answer is A,B or D

Answer 15

but i personally think it's B

Answer 16

i might be wrong

Answer 17

hm not quite

since all the x-values are linear (increasing by the same amount/decreasing by the same amount each time) we only need to check the y-values

so see which answer choice has the y-values change by the same amount each time (adding the same amount or subtracting the same amount)

Answer 18

A or C to me

Answer 19

hm not quite

let's look at the y-values of A
it goes from 2 to 1, so that's subtracting 1
it goes from 1 to 0, still good, subtracting 1 again

but it goes from 0 to 1, that's adding, not subtracting, so it's not linear

same reasoning with C

have you tried looking at D yet?

Answer 20

D seems to appears for subtracting

Answer 21

well, since it goes from -5 to -7/2 that's adding 3/2
going from -7/2 to -2 that's also adding 3/2
same thing from -2 to -1/2 and -1/2 to 1

so since the same value is being added each time D is linear and thus the appropriate solution

Answer 22

this question i've had a problem cause it asks what are the areas of the squares now i could be but i'm suggesting that the answer is C

Answer 23

sorry for the crappy diagram but let's pretend all the pink shapes are squares and the center is a right traingle

Answer 24

the side lengths of the three squares are thus, 16, 20, and 12

since area = side length^2 what will the three areas be?

Answer 25

B

Answer 26

good

Answer 27

I PICKED CAUSE I BELIEVE THIS IS THE CORRECT ANSWER

Answer 28

A

Answer 29

hm, not quite, let's try completing the square

first step: we start with the x term (36x), take 36, divide by 2 to get 18, and square it to get 324

we can then take the original expression x^2 + 36x = 88 and re-write this as

x^2 + 36x + 324 = 88

Answer 30

do you know how to then, factor the left side x^2 + 36x + 324?

Answer 31

** made a typo, should be x^2 + 36x + 324 = 88 + 324 since we need to add 324 to both sides

Answer 32

C

Answer 33

good

Answer 34

any ideas? as a hint they both have the same side lengths just in different orientations

Answer 35

A

Answer 36

good attempt but a reflection won't do it, it has to be a rotation judging by how they're positioned

should it be a 90 degree or a 180 degree rotation?

Answer 37

90 degree

Answer 38

good so B is the best sol'n

Answer 39

so if a^2 + b^2 = c^2 where a b and c are the lengths of the squares what do you think might be the best way to prove the theorem?

Answer 40

write down all givens and

Answer 41

well, if c^2 = a^2 + b^2 we are adding the areas of the two squares, right? so which answer choice best reflects this idea?

Answer 42

C

Answer 43

good

Answer 44

non-linear = not a perfectly straight line = which answer choice do you think it might be?

Answer 45

B

Answer 46

hm not quite

if you look at A there's a decrease of 1 unit by 1 unit but then it decreases 1 unit for every 4 x-units

so A is the one that's not a perfectly straight line, so A is the best solution in this case

Answer 47

i just figured out the answer is D

Answer 48

hm? I think the shapes are congruent, if you look at the dimensions they both have the same side lengths

Answer 49

which should narrow us down to A and C

Answer 50

so the answers is A

Answer 51

hm not quite, a 180 rotation would look like this

if you go through the transformations choice C would be the better option

Answer 52

for the pythagorean question, remember that the shapes must be three squares surrounding a right triangle

Answer 53

rectangles don't count

Answer 54

D

Answer 55

hm not quite, notice how D has a rectangle that is 4*5

see how choice B has a 3*3 square, a 4*4 square, and a 5*5 square? choice B is the only viable option in this question

Answer 56

any ideas? as a hint which one can you re-write in y = mx + b form?

Answer 57

A

Answer 58

good

Answer 59

I thought about C

Answer 60

good attempts but not quite

let's start w/ what we have x^2 = 6x + 12

we can subtract 6x from both sides to get

x^2 - 6x = 12

again, when completing the square, we take the x term (-6x), divide -6 by 2, square the result to get (-6/2) = -3 and (-3)^2 = 9 and add 9 to both sides

x^2 - 6x + 9 = 12 + 9

can you try factoring the left side and see which answer choice best fits this equation?

Answer 61

how do you factor (x^2 - 6x + 9)?

as a hint try picking two numbers that add up to -6 and multiply to get 9

Answer 62

x^2 - 6x + 9 factors into (x-3)^2 right?

so (x-3)^2 = 12 + 9 = 21

making B the best choice

Answer 63

RIGHT

Answer 64

basically you just want to pick the choice where the two shapes aren't congruent since the original question states the two triangles are congruent and it wants the one that is impossible

Answer 65

that's easy D

Answer 66

good

Answer 67

for a nonlinear function look for a choice where x has an exponent other than 1

Answer 68

D

Answer 69

good

Answer 70

well as stated before the squares should have side lengths that are equal to the sides of the triangle

that being said which choice makes the most sense? the side lengths of the triangle are 6, 8, and 10

Answer 71

B

Answer 72

good

Answer 73

well let's start by applying the distributive property to x(x-5) first, what do you get?

remember that A(B-C) = A*B - A*C try applying this logic to x(x-5)

Answer 74

B or D

Answer 75

D

Answer 76

x(x-5) = x^2 - 5x

giving us

x^2 - 5x - 10 = 0

completing the square

x^2 - 5x + 25/4 = 10 + 25/4

which does factor into D

Answer 77

well let's start by eliminating choices

do you think 11x - y = 15 is linear or nonlinear?

Answer 78

linear

Answer 79

awesome so that immediately eliminates C and D

between A and B which one do you believe is the more accurate/better reasoning?

Answer 80

B

Answer 81

awesome, so B is the best solution

Answer 82

well let's start by eliminating choices again

are shapes F and G congruent?

Answer 83

NO

Answer 84

hm, are you sure? they're both circles w/ diameter 4 and both have a quarter cut out of them

remember that rotations of the same shape are still considered congruent

that being said what might the best choice be?

Answer 85

oh i'm sorry it is i didn't look right

Answer 86

A

Answer 87

good

would you mind closing this question and opening a new one for your next questions? this thread has over 100 replies and its lagging a bit