Question

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMDk1MjM/G-CO.A.2%20Q2.JPG?ou=437405

Use the triangle on the grid above to answer this question.

Triangle LMN is reflected across the x -axis. Then it is reflected across the y -axis . Finally, it is translated according to the rule ( x + 7, y + 3) . What are the final coordinates of point M'?

A. (-4, -4)

B. (-10, -10)

C. (4, -4)

D. (10, 10)

Answer 1

@Vocaloid

Answer 2

original points of M are (3,7)

steps:
1. reflect across the x-axis by multiplying the y-coordinate by -1
2. reflect across the y-axis by multiplying the x-coordinate by -1
3 translate according to the rule (x+7,y+3)

lmk what your final result is

Answer 3

THE ANSWER IS C

Answer 4

good.

Answer 5

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMDk1MzM/G-CO.A.2%20Q3.JPG?ou=437405

Triangle HJK is translated according to the rule (x, y)-->(x - 3, y - 4). What are the coordinates of vertex H after this translation?

A. (-3, 3)


B. (3, -3)


C. (1, -2)


D. (-2, 1)

Answer 6

the original coordinate is (1,5) right? so what do you get when you apply the rule (x, y)-->(x - 3, y - 4)?

Answer 7

B.

Answer 8

hm not quite

the original x-coordinate is 1 right? and the rule says x - 3

so the new x-coordinate must be 1-3 = ?

Answer 9

-2

Answer 10

good so which option has -2 as the x-coordinate?

Answer 11

D.

Answer 12

awesome so D is your solution

Answer 13

A certain mapping in the xy-plane has the following two properties:

Each point on the line y=3x−2 maps to itself.
Any point P not on the line maps to a new point ​​P' in such a way that the perpendicular bisector of segment ​PP​′​​​​​is the line y=3x−2.

Which one of the following statements is true?

Choose 1 answer:

A. These properties define a reflection.


B. These properties define a rotation.


C. These properties define a translation.

Answer 14

hm. give me a moment, i'm not entirely sure what to make of the question yet.

Answer 15

let's try drawing it.

Answer 16

What does it look like to you?

Answer 17

@mikewwe13 "y = 3x -2 is a perpendicular bisector which means P and P' are the same distance from the line, just on opposite sides

so would that be a reflection rotation or translation?

Answer 18

reflection

Answer 19

good so choice A is the best

Answer 20

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMTM2MTU/G-CO.A.2%20Q5.JPG?ou=437405

Circle A' is the result of reflecting circle A across the line ℓ.

Select all of the correct statements about the unchanged properties of circle A and circle A, prime.

Choose all answers that apply:

A. Circle A and circle A​′ have the same area.


B. The radii of circle A and circle A​′ have the same lengths.


C. None of the above


D. Circle A and circle A​′ have the same circumference.

Answer 21

so if the circle is only being reflected and nothing else, that means it's the same size w/ the same proportions

with that being said which choice(s) do you think might apply?

Answer 22

B and D

Answer 23

that's a good start

if the circles have the same radii, then via A = pi * r^2 they must also have the same area

so choices A+B+D are your best bets

Answer 24

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMTcwOTk/G-CO.A.5%20Q1.JPG?ou=437405

Jerome reflected this figure over the line y = 2.

Which graph shows the result?

A. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q1b.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

B. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q1A.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE


C. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q1D.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE


D. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q1C.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

Answer 25

there we go, try reflecting each of the blue points across y = 2 (the horizontal line) to see what the final shape looks like

Answer 26

B.

Answer 27

hm not quite, B would be the line x = 2 (my mistake for drawing the wrong line)

Answer 28

oh no it's C

Answer 29

yup C well done

Answer 30

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMTcxMDk/G-CO.A.5%20Q2.JPG?ou=437405

Jacob transformed quadrilateral FGHJ to F'G'H'J'.

Which transformation did Jacob use?

A. reflection across the x -axis


B. reflection across the line x = 1


C. reflection across the y -axis


D. reflection across the line y = 1

Answer 31

any ideas? try imagining where the line of symmetry is that would cut the image in two equal halves

Answer 32

D.

Answer 33

hm, close, notice how you can draw a straight vertical line at x = 1 that splits the image in two equal halves

with that being said what's the best solution?

Answer 34

OK IT'S A

Answer 35

hm, not quite, the x-axis is y = 0

the line x = 1 is best represented with choice B

Answer 36

I thought of B the first time

Answer 37

https://learning.k12.com/d2l/common/viewFile.d2lfile/Database/MTAxMTcxMTg/G-CO.A.5%20Q3.JPG?ou=437405

Use the graph to answer the question.

Olivia reflects the triangle over the x-axis, then rotates it 90 degrees clockwise around the origin.

Which graph shows the resulting triangle?

A. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q3D.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

B. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q3C.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

C. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q3A.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

D. https://learning.k12.com/content/enforced/437405-COF_ID125380/G-CO.A.5%20Q3A.JPG?_&d2lSessionVal=RYzZrJchejAyWGAJd04IWOcKE

Answer 38

well you can either do this by drawing or by doing the calculations manually

either way, any ideas so far?

Answer 39

I BELIEVE it's B or D

Answer 40

reflecting across the x-axis gives us this:

Answer 41

it's B i had a feeling

Answer 42

then what do you get when you reflect 90 degrees clockwise?

Answer 43

not quite, choice B only shows the reflection not the rotation

Answer 44

hint - the triangle should be in QII

Answer 45

180

Answer 46

the new position would become of point M (h, k) then become M' (k, -h)

Answer 47

right so what would you get if you applied that rule to one of the points on the triangle? remember to use the after-image of the translation not the original triangle.

Answer 48

well, one of the points on the after-image is (-5,-4) right? (probably could have drawn that better ;-;)

so what do you get when you apply the rule (k, -h) to (-5,-4)?

Answer 49

i figured it out the answer to this A

Answer 50

this one, right? if so then well done

Answer 51

Point Q​′ is the image of Q(−5,1) under a translation by 6 units to the right and 2 units down.

What are the coordinates of Q​′ prime?

( _______ ,________ )

Answer 52

any ideas how you would write "6 units to the right" and "2 units down" in

(x + ____, y + ______) form?

Answer 53

(x + 6, y + 2)

Answer 54

close, "2 units down" means y - 2 not + 2 (+2 would be 2 units up)

so you have (x + 6, y -2) simply apply this to the point Q(−5,1)

Answer 55

(x + 6, y - 2) - Q(-5, 1)

Answer 56

hm, not quite, (x + 6, y-2) just means add 6 to x and subtract 2 from y

so you should get (-5 + 6, 1-2) just simplify to get your solution

Answer 57

1(1, -1)

Answer 58

good, make sure to enter 1 in the first blank and -1 in the second blank

Answer 59

1, -1 ?

Answer 60

yes

Answer 61

Point B​′​​(6,−5) is the image of B(−5,−2) under a translation.
Determine the translation.
Use non-negative numbers.

A translation by ___________ units to the (right or left) __________

and ___________ units (up or down) ____________

Answer 62

well let's take it one at a time

how would we get from 6 to -5? add, subtract, and by how much?

Answer 63

subtract

Answer 64

good, and how much would you subtract to get -5?

Answer 65

6 - ___ = -5

try filling in the blank

Answer 66

1

Answer 67

be careful with your signs

6 - 1 gives 5 not -5

6 - 11 gives -5 so we would say "11 units to the left"

Answer 68

same logic with -5 and -2

what would you add to go from -5 to -2?

Answer 69

-3

Answer 70

close, be careful with signs

you would have to add 3 to go from -5 to -2

so that would be a translation up by 3 units

I just realized it's asking from B to B' so we would just reverse the directions we stated before

so your solution is 11 units to the right and 3 units down

Answer 71

11 units to the (right or left) 3

Answer 72

11 units to the right
3 units down

Answer 73

i'm confused

Answer 74

A translation by ___________ units to the (right or left) __________

and ___________ units (up or down) ____________

Answer 75

yeah I wasn't very clear at the beginning

Point B​′​​(6,−5) is the image of B(−5,−2)

that means we are going from

B(−5,−2) to B​′​​(6,−5)

Answer 76

to go from -5 to 6, we add 11 to the x-coordinate which means 11 units to the right
to go from -2 to -5, we subtract 3 from the y-coordinate which means 3 units down

so you would put 11 in the first blank, select "right"
and put 3 in the second blank, select "down"

Answer 77

i can't select right or down

Answer 78

i goes along with it

Answer 79

uh :S can i see what your screen looks like?

Answer 80

anyway if it doesn't let you select right or down just fill in the blanks i guess

Answer 81

for the first blank, type 11
for the second blank, type right
for the third blank, type 3
for the fourth blank, type down