use matrices to determine the coordinates of the vertices of the translated figure. Triangle DEF with vertex matrix [7 -9 -1 -7 -3 -7] translated 1 unites left and 4 units down.

Use Matrices To Determine The Coordinates Of The Vertices Of The Translated Figure. Triangle DEF With

Answers

Answer 1

Answer:

(6, -11), (-10, -7) and (-2, -11)

Step-by-step explanation:

Coordinates of a triangle are represented in the form of a matrix as,

[tex]\begin{bmatrix}x_1 & x_2 & x_3\\ y_1 & y_2 & y_3\end{bmatrix}[/tex]

If the given triangle is shifted by 1 unit left and 4 units down,

Translation of vertices in the matrix form will be,

[tex]\begin{bmatrix}x_1 & x_2 & x_3\\ y_1 & y_2 & y_3\end{bmatrix}+\begin{bmatrix}-1 & -1 & -1\\ -4 & -4 & -4\end{bmatrix}[/tex]

For a triangle having vertices (7, -7), (-9, -3) and (-1, -7) when shifted 1 units left and 4 units down will be,

[tex]\begin{bmatrix}7 & -9 & -1\\ -7 & -3 & -7\end{bmatrix}+\begin{bmatrix}-1 & -1 & -1\\ -4 & -4 & -4\end{bmatrix}[/tex]

= [tex]\begin{bmatrix}7-1 & -9-1 & -1-1\\ -7-4 & -3-4 & -7-4\end{bmatrix}[/tex]

= [tex]\begin{bmatrix}6 & -10 & -2\\ -11 & -7 & -11\end{bmatrix}[/tex]

Coordinates of the triangle after the translation will be,

(6, -11), (-10, -7) and (-2, -11)


Related Questions

I really need help with this question, please!

Answers

Answer:

The triangles are not similar to each other .

7 Henri Plans to sell cups of coffe at his school sports event
Henri has a hot water Container that holds 16 litres.
He needs about 200ml of hot water for each cup of coffee
a How many cups of coffee can he make from a full bottle of
water. Hens will charge 80 cents per cup of coffee he hopes
to sell 250 Cups of coffee
How
many
full Containers of water will he use.
How much mony will he make ?​

Answers

Quantity of water with Henri = 16 litres

Quantify of water he will need for one cup of coffee = 200 ml

Number of cups of coffee he can make with a full cup of water :-

[tex] = 16 \: litres \: = 16000 \: ml[/tex]

[tex] = \frac{16000}{200} [/tex]

[tex] = 80 \: cups \: of \: coffee[/tex]

So , Henri can make 80 cups of coffee with one full bottle of water .

Quantity of water needed to make 80 cups of coffee = 16,000 ml

Quantity of water needed to make one cup of coffee :-

[tex] = \frac{16000}{80} [/tex]

[tex] = 200 \: ml[/tex]

So , 200 ml of water is needed to make one cup coffee .

Quantity of water he needs to make 250 cups of coffee :-

[tex] = 200 \times 250[/tex]

[tex] = 50000 \: ml[/tex]

So , Henri needs 50,000 ml of water to make 250 cups of coffee .

Number of water containers he will use :-

[tex] = \frac{50000}{16000} [/tex]

[tex] = 3.125 \\ = 3 \: water \: containers[/tex]

So , Henri will use 3 full water containers to make 250 cups of coffee .

Money charged per one coffee = 8 cents

Money charged for 250 coffees :-

[tex] = 250 \times 8[/tex]

[tex] = 2000 \: cents[/tex]

So , Henri will make 2000 cents if he sells 250 cups of coffee .

Therefore , Henri will use 3 full containers of water to make 250 cups of coffee and he he will make 2000 cents by selling 250 cups of coffee .

In a study of the television viewing habits of children, a developmental psychologist selects a random sample of 300 first graders - 100 boys and 200 girls. Each child is asked which of the following TV programs they like best: The Lone Ranger, Sesame Street, or the Simpsons.

Complete the following table:

Answers

Answer:

20, 50, 70, 110

Step-by-step explanation:

boys x simpsons: 20

girls x long ranger: 50

girls x simpsons: 70

total x sesame street: 110

have a great day :)

20 girls watch Long Ranger , 110 first graders watch Sesame Street , 20 boys watch Simpsons, and 70 girls watch Simpsons.

What is random sampling?

" Random sampling is a process of observing samples using such technique that each sample has equal probability."

According to the question,

As per the information of random samples given in the table,

Total number of boys are  = 100

Total number of girls = 200

For boys

Long Ranger + Sesame Street + Simpsons = 100

⇒  50 + 30 + Simpsons = 100

Number of boys view Simpsons = 100 - 80

                                                          = 20

In Long  ranger column,

50 Boys + ___girls = 100

Number of girls watching Long Ranger = 100 -50

                                                                   = 50

In Sesame street

30 boys + 80 girls = 110 Total viewers

Number of girls watching Simpsons = 90 -20

                                                            = 70

Hence, 20 girls watch Long Ranger , 110 total boys and girls watch Sesame Street , 20 boys watch Simpsons, and 70 girls watch Simpsons.

Learn more about random sampling here

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I need help because im not sure if im supposed to square it
[tex]2 \sqrt{x} = x - 3[/tex]

Answers

Step-by-step explanation:

[tex]2 \sqrt{x} = \: x - 3 [/tex]

[tex] ({ 2 \sqrt{x} )}^{2} = \: {x}^{2} - {3}^{2} [/tex]

[tex]4x = {x}^{2} - 9[/tex]

[tex] {x}^{2} - 4x - 9 = 0[/tex]

[tex]x = 5.60 \: and \: x = - 1.60[/tex]

2x80 pl help me ASAP if you can

Answers

Answer:

160

Step-by-step explanation:

help and explain if u can pls​

Answers

Answer:

C 60

Step-by-step explanation:

This is because if you do 303+60=363 and then you do 363/11 you get 33. So x=60

Answer:

60

Step-by-step explanation:

Multiply both sides of the equation by 11:

303 + x =363

Move constant to the right side and change its sign:

x = 363 - 303

Then,subtract the numbers:

x = 60

FIRST ONE TO AWNSER CORRECTLY GETS BRAINLEIST-1.8 + (2.1) Show your work

Answers

Answer:

0.3

Step-by-step explanation:

 2.1

-1.8

---------

0.3

someone please answer!

Answers

Answer:

m = -2

Step-by-step explanation:

To find the slope of a line, use the equation:

m = y2 - y1 / x2 - x1

Then, substitute in values:

m = 54 - 58 / 2 - 0

m = -4 / 2

m = -2

Answer:

c

Step-by-step explanation:

you need to count step by step

What is 24:28=? 250:400=? 270:30=? 4:80=? 55:33=? 1000:100=? 560:80=? 20:340=?


Plz help ill give u 20 points if u do all of these:)

Answers

Step-by-step explanation:

Ok so if you didn't know, : is another way to write / so 24:28 is the same thing as 24 divided by 28. Or if you just wanted to simplify to most, you just want to find the largest common factor and divide it by both.

24:28 = 6:7

250:400 = 5:8

270:30 = 9:1

4:80 = 1:20

55:33 = 5:3

1000:100 = 100:10

560:80 = 7:1

20:340 = 1:17

Answer: 24:28= 6:7

250:400= 5:8

4:80= 1:20

55:33= 5/3

1000:100= 10:1

560:80= 7:1

20:340= 1:17

Step-by-step explanation:

Divide the numbers on each side of the ratio by Common Factors until what's left can't be divided any further.

One example, last one:

20:340 both divisible by 10, so you get 2:34. Both even numbers so divide by 2. You get 1:17. They can't be divided any further to get whole numbers, so that's the answer.

3 less than one fourth of a number

Answers

Answer:

one fourth a number minus three

¼x-3

0.42 - 4) = 0.24 + 7)

Answers

Answer:

im sorry if not but i think its 7.24

Step-by-step explanation:

HELP ME SOLVE THE LAST ONE, IF THEYRE ALL WRONG CORRECT THEM, TYYYYYY

Answers

Answer:

they are right

Step-by-step explanation:

Answer:

you have the 4 and 7 backwards and the last one they r losing about .75 gallons hope this helps

2. Jack’s parents were planning a big birthday party for him. Answer the questions below. Show your work for all parts.
a. His parents spent $4.49 on each of 6 goodie bags. How much did they spend on goodie bags?

b. They spent $150 to rent a bounce house for 8 hours. How much is the hourly rate for the rental?


c. If the parents spent a total of $400 on everything for the party, how much more did they spend in addition to what was spent in parts (a) and (b)?

Answers

A. Do 4.49 times 6 B. Do 150 divided by 8 C. I belive you add the answers for A and B and then subtract that from 400 and then that’s your answer for part C

A. Do 4.49 times 6 B. Do 150 divided by 8 C. I belive you add the answers for A and B and then subtract that from 400 and then that’s your answer for part C

Simplify i31.

1
−1
i
−i

Answers

Answer:

D. -i

Step-by-step explanation:

I took the quiz and got a 100%

The required value of the complex number [tex]i^{31}[/tex] = -i.

Given that,
To determine the value of complex numbers [tex]i^{31}[/tex].

What is arithmetic?

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

What is a complex number?

The number that are constitute of real and imaginary numbers are called complex number. complex number can be represents as z = a+ ib ,where a = real part and bi = imaginary part.

Here,
[tex]i^4 = 1[/tex] and [tex]i^3 = -i[/tex]

For complex numbers [tex]i^{31}[/tex]

[tex]=i^{31}\\=(i^4)^7.i^3\\=1.-i\\=-i[/tex]

Thus, the required value of the complex number [tex]i^{31}[/tex] = -i.

Learn more about complex numbers here: https://brainly.com/question/28007020

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What is the solution of -28=22-5x?

Answers

Answer:

10=x

Step-by-step explanation:

google

Answer:

x=10

Step-by-step explanation:

Use Symbolab.com

Plz help question 1 or 2

Answers

Answer:

sorry dont know

Step-by-step explanation:

30 oite 904-=

Find the sum of the arithmetic sequence 22, 11, 0, -11, ..., –77.
A -198
B.-275
C. -297
D. -385

Answers

Answer:

B.

Step-by-step explanation:

First you need to figure out how many numbers there are, so with this you can simply count 10. Then use the formula to plug in the numbers: 10(22-77)/2 to get the answer.

The required sum of the arithmetic progression is -275.

The arithmetic sequence is given 22, 11, 0, -11, ..., –77, sum of the sequence is to be determined.

What is arithmetic progression?

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
first term (a) = 22
Last term (l) = -77

Now,
l = a + (n - 1)d
-77 = 22 + (n - 1) *(-11)
-77 - 22 = (n - 1)(-11)
n - 1 = 9
n = 10

Now,
sum of the arithmetic sequence,
s = n / 2 [a + l]
s = 10 / 2 [22 - 77]
s = 5 [-55]
s = -275

Thus, the required sum of the arithmetic progression is -275.

Learn more about arithmetic progression here: https://brainly.com/question/20334860
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Who Smokes More: Male Students or Female Students?

Information on a sample of 362 college students is collected. The complete dataset is available at StudentSurvey. We see that 27 of the 193 males in the sample smoke while 16 of the 169 females in the sample smoke

Answers

the male smoke more

Step-by-step explanation:

the male smoke more because 27 out of 193 and 16 out of 169 females smoke

Asa spent $165.20 on 5 video games. If the video games each cost the same amount, how much did one video game cost?

Answers

Answer:

the answer is $33.04

Step-by-step explanation:

since the total cost was $165.20 and we need to find the cost of one  video game we will divide the the total ($165.20) with 5 video games and you will get $33.04

To what subset(s) of the real numbers does the
number - 0.45 belong? Explain your answer.

Answers

Answer:

Integers, and rational, I know this because -0.45 is a negative number   and because rational numbers include all categories.

Step-by-step explanation:

Katie bought a new dress for the winter
formal dance at school. She was able to find it
on sale for 40% off the original price. If she
paid $72 after the discount was applied, then
what was the original price of the dress?

Answers

Answer: it’s 120

Step-by-step explanation:

the triangular prism below has equilateral bases with sides of 4 in and a height of 4.5 in and rectangular sides measuring by 4 in by 7in what is the lateral surface area of the prism?

Answers

Answer:

quite not sure

Step-by-step explanation:

Quadrilateral ARMY is rotated 90° about the origin.

Answers

Answer:

what's the question??

Evaluate
5
9
÷
5
18
jjijijij
kok

Answers

Answer:

i cant even see the words

Step-by-step explanation:

sorry i cant help

If it’s 59 divided by 518 than it’s 0.1138

help please i will give brainliest

Answers

The 10x + 5 = 35 goes first I think

Then the 35x + 5 = 10 goes second and then

Then 5x+ 10 = 35 goes last

What equation mathches this situation John had 10$. He spent x dollar now he has $3.20

Answers

Answer:

$6.80

Step-by-step explanation:

You would need to subtract $10-$3.20 to find out how much he spend and that is how you will get your total

Answer:

$6.80

Step-by-step explanation:

10-3.20

Please everybody! Can you guys help me? This is super urgent!
Rae pays $48 for a 12-month magazine subscription. How much does Addison pay per month? Thank you!

Answers

Answer:

$4

Step-by-step explanation:

Divide $48 by 12

(Because there are 12 months in a year)

Your answer is $4

$48 divided along 12 months = $4

Hope I helped :)

Please consider Brainliest :)

Answer:

$4

To find the amount Rae pays each month, we have to divide 48 by 12 (because there are 12 months in a year.)

48 ÷ 12 = 4.

Answer = $4.

Hope this helps!

Twice the sum of three and a number is 30. Find the number

Answers

9514 1404 393

Answer:

2(x +3) = 3012

Step-by-step explanation:

When x represents the number, "the sum of 3 and a number" is (x+3). Twice that sum is 2(x+3). "Is 30" means this expression is equal to 30:

  2(x +3) = 30 . . . . an equation for the given conditions

__

We can solve this equation by dividing by 2:

  x + 3 = 15

  x = 12 . . . . . . subtract 3

The number is 12.

Genevieve has $9000 to invest. She invests some at 6% annual interest and the rest at 4% annual interest. After one year, her total interest from both accounts is $444. How much did she invest in each account? (Clearly label which amount is for which account in your answer. Hint: Over a one year period, annual interest is the same as simple interest.)

Answers

Answer:

The first account, she invested = $4200 and in the second = $4800

Step-by-step explanation:

Let us assume that Genevieve invests $x at 6% ,

Hence, she invests ($9000 - $x ) at 4% ,

It's given that the combined interest from both of the above accounts is $444,

So,

0.06x + 0.04 (9000 - x) = 444

=> 0.06x + 360 - 0.04x = 444

=> (0.06x - 0.04x) + 360 = 444

=> 0.02x = 444 - 360

=> 0.02x = 84

=> x = 84/0.02

=> x = 8400/2 (By multiplying the denominator and numerator)

=> x = 4200

Therefore, 9000 - x = 9000 - 4200 = 4800

$4200 at 6% and $4800 at 4%

Therefore, the first account, she invested = $4200 and in the second = $4800

If my answer helped, kindly mark me as the brainliest!!

Thank You!!

Find the distance between the two points in simplest radical form.
(1,5) and (-5,8)

Answers

3 square root of 5 or ≈ 6.70820393249937
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