Question

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What is the name of the line of reflection for the pair of figures?

Enter your answer in the box.

line _________

Answer 1

@Vocaloid

Answer 2

any ideas? which line is in the exact center of the two images and produces the reflection?

Answer 3

line r

Answer 4

good (make sure to only enter "r" in the box)

Answer 5

https://static.k12.com/nextgen_media/assets/8078760-NG_GMT_SemA_01_UT_11.png

A. Translation
B. Reflection
C. Rotation

Answer 6

any ideas? notice how the two shapes are symmetric about an imaginary line

Answer 7

REFLECTION

Answer 8

good

Answer 9

https://static.k12.com/nextgen_media/assets/8078761-NG_GMT_SemA_01_UT_12.png

A. Translation
B. Reflection
C. Rotation

Answer 10

any ideas? notice how the orientation of the shape has changed 90 degrees

Answer 11

the answer is translation

Answer 12

hm, not quite, translation would not change the orientation of the shape

out of those three options ~rotation~ is the only one that could change the orientation 90 degrees

Answer 13

https://static.k12.com/nextgen_media/assets/8078762-NG_GMT_SemA_01_UT_13.png

A. Translation
B. Reflection
C. Rotation

Answer 14

the answer is translation for sure

Answer 15

or reflection

Answer 16

hm, not quite, a translation keeps the original image in the same orientation

notice how the two triangles are facing opposite directions, like they have been turned around 180 degrees

that being said what is the best choice?

Answer 17

rotation

Answer 18

good

Answer 19

https://static.k12.com/nextgen_media/assets/8078763-NG_GMT_SemA_01_UT_14.png

A. Translation
B. Reflection
C. Rotation

Answer 20

any ideas? notice how the two triangles are in the same orientation this time

Answer 21

REFLECTION

Answer 22

hm not quite

remember, a ~translation~ will preserve the original orientation of the image

Answer 23

translation i apologize

Answer 24

good, translation is your sol'n

Answer 25

https://static.k12.com/nextgen_media/assets/8078786-NG_GMT_SemA_01_UT_03.png

Luisa draws a regular nonagon and rotates it about its center.



Which angle measures can Luisa rotate the regular nonagon through to map it onto itself?



Select each correct answer.

A. 40°

B. 80°

C. 90°

D. 120°

E. 160°

F. 180°

Answer 26

well there's one obvious choice: if we take 360 degrees, divide by the number of sides 9, we get 360/9 = 40 degrees as one possibility

you can also rotate any multiple of 40

so with that being said what might the best choices be?

Answer 27

A, C, E, and F

Answer 28

not quite

90 and 180 are not multiples of 40
remember the process for finding multiples:

40*1 = 40
40*2 = 80
40*3 = 120
40*4 = 160

Answer 29

A, B, D, and E

Answer 30

good

Answer 31

https://static.k12.com/nextgen_media/assets/8078766-NG_GMT_SemA_01_UT_20.png

Solve for x.


Enter your answer in the box.

x = _______°

Answer 32

this is a 6-sided figure

so use the formula (n-2) * 180 where n = 6, to find the sum of interior angles

then subtract all the angles that are already in the shape

Answer 33

(6-2) x 180 = 720.

Answer 34

then do the angles you have add up to 588 ?

Answer 35

good, so 720 - 588 gives you 132 as the missing angle so 132 is the sol'n

Answer 36

What is the measure of an exterior angle of a regular 13-sided polygon?



Enter your answer as a decimal in the box.

Round to the nearest tenth of a degree.


________°

Answer 37

exterior angle is always 360/the number of sides

Answer 38

360/13 ?

Answer 39

yes, and that gives us 27.7 when you plug into a calculator

Answer 40

so i put 27.7 ?

Answer 41

yes.

Answer 42

https://static.k12.com/nextgen_media/assets/8121192-GA_GMT_UT_A1_NP100_236.jpg

Trapezoid W′X′Y′Z′ is the image of trapezoid WXYZ under a dilation through point C.

What scale factor was used in the dilation?


A. −6/5

B. −5/6

C. 5/6

D. 6/5

Answer 43

they give you two corresponding sides, 18 WX and 15 W'X'

since we want the factor from WX to W'X', we divide the length of W'X' over WX

so 15/18 --> simplify this fraction to get your solution

Answer 44

5/6

Answer 45

good

Answer 46

https://static.k12.com/nextgen_media/assets/8121195-GA_GMT_UT_A1_DP100_237_002.jpg

The dashed triangle is the image of the solid triangle. The center of dilation is (−5, 7) .



What is the scale factor used to create the dilation?

Enter your answer as an integer or decimal in the box.


_______

Answer 47

i believe the answer is 0.25

Answer 48

well, the two triangles are in opposite directions so our scale factor is negative

let's compare two corresponding sides of the triangle (the shorter sides, for example)

the shorter side of the image is 2
the shorter side of the pre-image is 8

so image/after-image = ?

Answer 49

hm, not quite, -0.25 since the triangles are in opposite directions

Answer 50

The scale factor is h₂/h₁ = 2/8 = 1/4 = 0.25
Also, the scale factor is w₂/w₁ = 3/12 = 1/4 = 0.25 therefore making the answer

Answer 51

but due to both of our calculations It is actually -0.25, because the image and pre-image are opposite to each other. you're correct

Answer 52

good, -0.25

Answer 53

Select from the drop-down menus to correctly complete the statement.

The rule (x, y)→(x − 6, y − 7) represents a translation 6 units ________ and 7 units _________.

A. left

B. right

C. up

D. down

Answer 54

any ideas? do negative signs mean up or down? left or right?

Answer 55

up

Answer 56

hm not quite

in the x-direction, negative sign means left
in the y-direction, negative sign means down.

Answer 57

i'm sorry

Answer 58

1. left

2. down

Answer 59

good

Answer 60

The coordinates of the vertices of △DEF are D(2, −1) , E(7, −1) , and F(2, −3) .

The coordinates of the vertices of △D′E′F′ are D′(0, −1) , E′(−5, −1) , and F′(0, −3) .



What is the sequence of transformations that maps △DEF to △D′E′F′ ?



Drag and drop the answers into the boxes to correctly complete the statement.

A sequence of transformations that maps △DEF to △D′E′F′ is a ________ followed by a _________.

A. translation 2 units right

B. rotation of 180° about the origin

C. reflection across the y-axis

D. translation 2 units up

Answer 61

hm

any attempts to draw this out?

Answer 62

the sequence of transformations that maps △DEF to △D′E′F′ are reflection across the y-axis and translation 2 units right.

Answer 63

good that's correct

Answer 64

https://static.k12.com/nextgen_media/assets/8078759-NG_GMT_SemA_01_UT_05.png

What is the correct classification for each given angle?



Drag and drop the answer into the box to match each angle.

∠NPL

Answer 65

it was supposed to be arrows

Answer 66

yeah I got it

anyway any ideas? notice how <NPL is on a straight line
<JPL is greater than 90
and
<NPK is exactly 90

with that said what are the three choices?

Answer 67

NPL is a straight line.
JPL is an obtuse angle
NPK is a right angle

Answer 68

good

Answer 69

any ideas? as a hint you can start w/ a counterclockwise 90 degree rotation

Answer 70

When we rotate a figure of 90 degrees counterclockwise, each point of the given figure has to be changed from (x,y) to (-y,x)

Answer 71

good, then after you apply that rule to the shape, what transformation do you need to do ?

Answer 72

graph the rotated figure

Answer 73

like, we applied a 90 degree counterclockise rotation right? after you apply this, we still need to do one more transformation to get the shape into the dotted shape position

would it be at translation, reflection, or rotation?

Answer 74

rotation

Answer 75

hm not quite

notice how after you do the rotation, the triangle is in the right orientation

so all you have to do is translate it to get it into the dotted position

Answer 76

how much left/right or up/down do you have to translate it?

Answer 77

up/down

Answer 78

how many units?

Answer 79

3 units

Answer 80

be careful

let's just look at point A

after the rotation you get

A = (-2,-1)

now, the after-image has A" as (2,0)

how many units across do you have to translate?
how many units up?

Answer 81

-3

Answer 82

or 4

Answer 83

let's just look at the x-coordinates

how much do you have to add to go from -2 to 2?

Answer 84

wait i see now

Answer 85

how much do you have to add to get from -2 to 2? the solution is not 2

-2 + ___ = 2

fill in the blank

Answer 86

4

Answer 87

good so there's a translation 4 units to the right

now let's look at the y-coordinates

what do you have to add to get from -1 to 0?

Answer 88

1

Answer 89

good

so the sequence of transformations is

1. a 90 degree counterclockwise rotation and
2. a translation right 4 units and up 1 unit

now, that's the problem in words, but it also asks for an ordered pair rule, how would you go about doing that?

Answer 90

1. 2 IS FOR A ?

Answer 91

???

Answer 92

1. a 90 degree counterclockwise rotation and
2. a translation right 4 units and up 1 unit

THAT'S just for A right ?

Answer 93

yes

Answer 94

then for b) write the ordered pair rule.

Answer 95

Transformation one is (x, y) -> (-y, x)
Transformation two is (x, y) -> (x + 2, y)

Answer 96

remember what we said before. 4 units to the right. 1 unit up. how would we represent that in ordered pair form?

Answer 97

An ordered pair tells you how many units left and right you move (the x value) and how many units up and down you move (the y value) from the origin (where the x & y lines meet in the middle).

Answer 98

fill in the blank:

"a translation 4 units to the right can be represented as x + ___"

Answer 99

1

Answer 100

"4 units to the right" so naturally we would represent this as "x + 4"

repeat this logic with the y-coordinates

"a translation 1 unit up would be represented as y + ___"

Answer 101

1

Answer 102

good

so the ordered pair rule is (x,y) --> (x+4,y+1).

Answer 103

i'm sorry for not getting it right, btw i pressed 1 by accident i meant 4

Answer 104

alright

well you have the rule

(x+7, y-3)

for a) apply this rule to the point (-10,0)

Answer 105

10

Answer 106

(x+7, y-3)

means add 7 to the x-coordinate
subtract 3 from the y-coordinate

your answer should be a coordinate point, not just 1 number.

Answer 107

i'm having a lil bit of trouble with solving

Answer 108

you have the point (-10,0)

-10 is the x-coordinate
0 is the y-coordinate

follow these directions:

add 7 to the x-coordinate
subtract 3 from the y-coordinate

Answer 109

-10 + 7 = -3
0 - 3 = -3

(-3, -3)

Answer 110

good

so for blank 1 you would just say (-3,-3)
and for blank 2 you would show your calculations

-10 + 7 = -3
0 - 3 = -3

Answer 111

then for blanks 3 and 4 repeat this process with the point (-7,3)

use the same rule as before.

Answer 112

-7 + 7 = 0

3 - 0 = 3

Answer 113

x-coordinate is good
for the y-coordinate we are subtracting 3 not 0

so 3 - 3 = 0

so for blank 3 your coordinate is (0,0)
and for for blank 4 your calculations could be

-7 + 7 = 0
3-3 = 0
(0,0)

Answer 114

for blank 5) do you think the transformation is a function?

remember, to be a function, it must give each input only one unique output

Answer 115

what do you think ?

Answer 116

what's this about senators?? we are talking about a person writing controls for a video game

Answer 117

cancel that out

Answer 118

yes it is a function because it must give each input only one unique output and an input is the independent value so meaning for each input, there will only be one output.

Answer 119

it's a bit garbled

"yes it is a function because it gives each input only one unique output"
should be sufficient.

Answer 120

so for blank 5 write "yes" and for blank 6 write the explanation.

Answer 121

anyway we should probably close this because it's already 100+ replies