A coordinate plane is shown. Triangle PQR has vertices P at negative 6 comma 6, Q at negative 6 comma 3, and R at negative 3 comma 3. Triangle P prime Q prime R prime has vertices at P prime negative 2 comma 2, Q prime at negative 2 comma 1, and R prime at negative 1 comma 1. What is the scale factor of dilation?


Answer 1


The scale factor of dilation from ΔPQR to ΔP'Q'R' is 1/3

Step-by-step explanation:

The given information are;

The vertices of ΔPQR are;

P(-6, 6), Q(-6, 3), and R(-3, 3) and the coordinates of ΔP'Q'R' are P'(-2, 2), Q'(-2, 1), and R'(-1, 1)

Given that the length, l, of each side of the triangles is given by the formula for calculating length given the vertices we have;

[tex]l = \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}[/tex]

For side PQ, we have;

(x₁, y₁) = (-6, 6), (x₂, y₂) = (-6, 3)

Given that the points have equal y-values, the length is the difference of their x-values as follows;

[tex]l_{PQ}[/tex] = 6 - 3 = 3

Similarly, length QR is the difference in the y-values, since the x-values are equal. therefore, we have;

[tex]l_{QR}[/tex] = -3 - (-6) = 3

Length PR is given as follows;

(x₁, y₁) = (-6, 6), (x₂, y₂) = (-3, 3)

[tex]l_{PR} = \sqrt{\left (3-6 \right )^{2}+\left (-3-(-6) \right )^{2}} = \sqrt{18} = 3\cdot \sqrt{2}[/tex]

[tex]l_{PR}[/tex] = 3·√2

For P'Q', we have

P'(-2, 2), Q'(-2, 1)

[tex]l_{P'Q'}[/tex] = 2 - 1 = 1

[tex]l_{P'Q'}[/tex] = 1

For Q'R', we have

Q'(-2, 1), R'(-1, 1)

[tex]l_{Q'R'}[/tex] = -1 - (-2) = -1 + 2 = 1

[tex]l_{Q'R'}[/tex] = 1

For P'R', we have;

P'(-2, 2), R'(-1, 1)

[tex]l_{P'R'} = \sqrt{\left (1-2 \right )^{2}+\left (-1-(-2) \right )^{2}} = \sqrt{2} = \sqrt{2}[/tex]

[tex]l_{P'R'}[/tex] = √2

Therefore, given that we have

PQ/(P'Q') = PR/(P'R') = 3/1 = 3 and QR/(Q'R') = 3·√2/(√2) = 3

The scale factor of dilation from ΔPQR to ΔP'Q'R' = 1/3.

Related Questions

5y-30=-5y+30 and also can you show the steps :}



add 30 to both sides

5y = -5y+60

add 5y to both sides

10y = 60

divide both sides by 10

y = 6

hope this helps!

3-4 what is the answer I am dumb plz helq



Its -1. Do not call yourself dumb, though, negatives are the easiest subject

Step-by-step explanation:

loll it’s -1 ! don’t worry you’re not stupid

The original price of a play ticket was $36.00. Yolanda bought the ticket at original price and then marked it up 10% and resold the ticket. How
much did she resell the ticket for?


she sold the ticket for $39.50
explanation: you take 36 and time it by 10% and it will give you $3.60 and you add it to 36

In the image above, what do the red arrows on lines mean?


Answer: ............................Step-by-step explanation:You need to attach an image

Evaluate 3{5 + 3[10 + 4.8]}​




Step-by-step explanation:

Determine if the function shows a linear relationship or an absolute value relationship. Then evaluate the
function for the indicated value of x.
A. f(x) = |x-31-2; x = -5
B. g(x) = 1.5x; x = 0.2
C. p(x) = 17 - 2x]; x = -3


I think it’s B because it’s negative




1. 30

2. 0.83333333

3. 1.2

4. 30

Step-by-step explanation:

H is the only reasinable decimal

The U.S. Capital building includes a statue on top representing freedom. If a person stood outside the building with a direct line-of-sight of 983 feet to the top of that statue and an angle of elevation of 17o , what would be the distance from the ground below the statue to the top of the statue?



ok u need to list the numbers in the journal

Step-by-step explanation:

that doesn't give the answer



what doesnt give the answer??

Step-by-step explanation:

Solve proportion 2/4.5=t/0.5


0.2 or 2/9 in fraction form I believe.

XY−→− bisects ∠WXZ and m∠WXY=29∘. Find m∠ZXY and m∠ZXW.



29° and 58°

Step-by-step explanation:

Since XY bisects ∠ WXZ then ∠ WXY and ∠ ZXY are congruent, thus

∠ ZXY = ∠ WXY = 29°

∠ ZXW = ∠ WXY + ∠ ZXY = 29° + 29° = 58°

Which inequality matches the graph shown?



I am pretty sure it is x>8 which is B.

Step-by-step explanation:

I’m one hundred percent positive it’s B because if it’s open the aren’t less then or equivalent to or greater than or equivalent to

On a flight from New York to London, an airplane travels at a constant speed. An equation relating the distance traveled in miles, d, to the number of hours flying, t, is LaTeX: t=\frac{1}{500}dt=1500d. How long will it take the airplane to travel 800 miles?




Step-by-step explanation:

We know that Speed= distance/ time

But from the question, An equation relating the distance traveled in miles d to the number of hours flying t is t= 1/500d.

And the distance is given as 800 miles

Then, what we need is to substitute the given Distance into the equation of time.

t= 1/500d. Where d= 800 miles

t= (1/500) × 800 miles

t= 800 miles/500

t= 1.6hours

Hence, it will take the airplane to travel 800 miles , 1.6hours

a cubic block of ice has a volume of 1,331 inches how tall is the block



The answer is 11. 11^3 is 1,331.

Step-by-step explanation:


The length of a rectangle is 11 less than 9 times the width. The perimeter of the rectangle is 18 inches


Length = 7   Width = 2

Step-by-step explanation:

L = Length

W = Width



2(9W-11) + 2W = 18

18W - 22 +2W = 18

20W -22 = 18

20W = 40

W = 2

L = 9(2)-11



you are listening to a playlist that has three hip hop songs 2 rock songs if they are a 15 more songs on this playlist and the ratio of hip hop song or rock song stayed the same how many of each type would be on this playlist ​


doing this fa points , sorry not sorry .

Apply the Triangle Sum Theorem, and solve for x.
5x° (Angle G)
4xº(Angle H)
3xº(Angle J)




Step-by-step explanation:





m= 4/5 - 2/5
————- = ?
-1 - -2



2/5 = 4/5 - 2/5 = m

Steven sells bags of different kinds of cookies. He made $27 selling bags of Oreos, $18 selling chocolate chips cookies, and $45 selling chunky sugar cookies. Each bag of cookies costs the same amount. What is the most that Steven could charge for each bag of cookies?



9 dollars

Step-by-step explanation:

It would be 9 dollars because that is the only common factor that could go into 27, 28, or 45.

Help with these math questions grade 12



1. 15.1%

2. 8.3%

3. 12%

4. 25%

Step-by-step explanation:


percent change = (new number - old number)/(old number) * 100%

percent change = (21300 - 18500)/(18500) * 100%

percent change = 15.1%

A positive percent change is a percent increase.

Answer: The percent increase is 15.1%.


percent change = (new number - old number)/(old number) * 100%

percent change = (298000 - 325000)/(325000) * 100%

percent change = -8.3%

A negative percent change is a percent decrease.

Answer: The percent decrease is 8.3%.


percent change = (new number - old number)/(old number) * 100%

percent change = (110 - 125)/(125) * 100%

percent change = -12%

A negative percent change is a percent decrease.

Answer: The percent decrease is 12%.


percent change = (new number - old number)/(old number) * 100%

percent change = (1500 - 2000)/(2000) * 100%

percent change = -25%

A negative percent change is a percent decrease.

Answer: The percent decrease is 25%.

what is the answer for −3x−6+(−1)


Hi it would be -9x-1 hope that helps



Step-by-step explanation:

Combine like terms

-6+-1 = -6-1 = -7

Hence, it's -3x-7

Joe and Carmen are partners in a business. Joe makes $2.00 profit for every $5.00 profit that Carmen makes. If Carmen makes $20 on the first item they sell, how much profit will Joe make?


Joe will make a $8.00 profit

people wont solve my question i need it ASAP



A pig has 10,000 kg mass more than a mass

Step-by-step explanation:


When Arjun makes hot cocoa, he adds 20\text{ mL}20 mL20, start text, space, m, L, end text of chocolate syrup for every 333 ounces of hot water. Arjun's brother, Eli, adds 45\text{ mL}45 mL45, start text, space, m, L, end text of chocolate syrup for every 666 ounces of hot water. Which hot cocoa is more chocolatey? Choose 1 answer: Choose 1 answer:



45mL hot cocoa is more chocolatey

Step-by-step explanation:

When Arjun makes hot cocoa, if he add 20mL of chocolate syrup to 3ounces of water, let us know the equivalent chocolate in one ounces of water.

20mL = 3 ounces

x = 1 ounce

cross multiply

3x = 20

x = 20/3

x = 6.67 mL

This means he must have add 6.67mL of chocolate to 1 ounce of water.

Similarly, if 45mL is added to every 6 ounces

45mL = 6ounces

x = 1 ounce

cross multiply

6x = 45

x = 45/6

x =  7.5mL

This means he must have add 7.5mL of chocolate to 1 ounce of water.

The hot cocoa that is more chocolatey is the one with the highest amount of chocolate in 1 ounce. That is 45mL hot cocoa


eli's cocoa is more chocolately. i would show proof (on khan academy), but I just skipped the q. :|

Step-by-step explanation:

Write 2.08 x 10^2 in standard form.​




Step-by-step explanation:

If you multiply 2.08 by ten to the second power (100) Then you get 208

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  The given expression can be written in the standard form as 208.

What are Scientific notations?

Scientific notations are the way through which a very small or a very large number can be written in shorthand.  In scientific notations when a number between 1 and 10s is multiplied by a power of 10.

For example, 6,500,000,000,000 can be written as 6.5e+12.

The given expression can be written in the form of an expression as shown below.

2.08 x 10²

= 2.08 × 100

= 208

Hence, the given expression can be written in the standard form as 208.

Learn more about Scientific notation here:



What single decimal multiplier would you use to decrease by 6% followed by a 19% increase?


Answer: 13% increase?

Step-by-step explanation: 19-6=13 which means it would be 1.13 the original amount?



Step-by-step explanation:

A 6% decrease would be 0.94 and a 19% increase after that would be 1.13

Convert y = x2 - 4x + 1 to vertex form by completing the square.

O y= (- 1)2 + 4
O y= (1 - 2)2 +5
O y= (x - 2)2 – 3
O y = (x - 4) + 1



vertex: (-2, -3)

Step-by-step explanation:

y = x2 + 4x                 + 1  

y = x2 + 4x + 22          + 1 - 22  

y = (x + 2)2 + 1 - 4  

y = (x + 2)2 - 3            in y = (x - h)2 + k, (h, k) is the vertex.  



y = (x - 2)² - 3

Step-by-step explanation:


y = x² - 4x + 1

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 1

   = (x - 2)² - 3

if the cost of carpeting a floor is $2.50 per foot how much will it cost to carpet a rectangular floor that is 10 feet by 12 feet



300 dollars

Step-by-step explanation:

Multiply 10 feet by 12 feet to get the total number of feet needed

10x12=120 feet

120 times $2.5= $300

The cost to carpet a rectangular floor is $300.

Given that,

The cost of carpeting a floor is $2.50 per foot A rectangular floor that is 10 feet by 12 feet

Based on the above information, the calculation is as follows:

[tex]= 10 \times 12 \times \$2.50[/tex]

= $300

Learn more: brainly.com/question/17429689





Step by step

determine the defined range

remove parentheses

move the terms

collect like terms and calculate

divide both sides

I need help what is -0.5 _ -0.2​


-0.5 < -0.2,
because I need more characters
Other Questions
What is a taiga?O 1/5O 2/5O 3/5O 4/5 13In the figure shown below, if line mis parallel to line n, then find the value of x. (This is a 2 part question.)m(2x-10)(65 - x)Part AWrite the equation to find the value of x. (DO NOT find x, just write the equation.)(2x - 10) (65 - x)Part BWhat is the value of x?Y One of the dog treats in Shelleys shop is 8 inches long and 3.2 inches wide. She wants to make a miniature version that has proportional dimensions. If the miniature treat will be 3 inches long, how wide should it be? What is the meaning of this excerpt?Reread this excerpt from The Call of the Wild.An oath from Perrault, the resounding impact of a clubupon a bony frame, and a shrill yelp of pain, heralded thebreaking forth of pandemonium. The camp wassuddenly discovered to be alive with skulking furryforms,-starving huskies, four or five score of them,who had scented the camp from some Indian village.They had crept in while Buck and Spitz were fighting,and when the two men sprang among them with stoutclubs they showed their teeth and fought back. Theywere crazed by the smell of the food. Perrault found onewith head buried in the grub-box.O Perrault is fighting stray dogs that have invaded thecampsite looking for food.O Perrault is punishing members of his dogsled teamfor their aggressive acts.Perrault is reprimanding his dogsled team for stealingscraps of food.O Perrault is feeding wild dogs and training them forwork on his team. (4.3 x 10^-3)(2 x 10^-2) in standard form PLEASEEEEEEQu palabra describe mejor el proceso de independencia de Mxico? The zika virus was first identified in Uganda in 1947. The virus is transmitted from person to person by a bite from a mosquito. It is commonly carried by the Aedes mosquito which is prevalent throughout Central Africa. The virus has more recently spread to the Americas (South, Central, and now North) and is expected to spread to Europe. There is a concern that the virus may reach epidemic proportions. Zika virus is related to yellow and dengue fever. Common symptoms are low grade fever and a distinctive skin rash and other symptoms include vomiting, headache, and muscle and/or joint pain. Pregnant women should avoid traveling to areas known to have zika virus present because the virus is known to cause microcephaly and developmental difficulties related to the central nervous system. Based on the paragraph above, class discussions, and other VALID (be careful with your selection of e-materials! CDC Center for Disease Control is a good place to start) sources of information please answer the following questions. 1. State a reason why the virus has spread to the Americas and likely to spread to Europe. 2. Define the term microcephaly.3. What bones of the fetal skull would be affected by zika? Specifically, what area of the CNS is not fully developed in microcephalic individuals. Why was the Stamp Act a cause of the American Revolution? A hospital administrator emailed an agenda to all the staff employees for an upcoming meeting. The agenda listed thepoints below.-Discuss the change in policy for dealing with patient privacy rights.-Discuss the possible solutions to overcrowding in the waiting rooms.-Discuss possible fundraising ideas for the purchase of a spectrophotometer.What part of the meeting is being effectively communicated to staff members?the timeliness of the meetingthe objectives of the meetingthe meeting minutesthe administrator's negotiation skills Carlos sold 6 cellphones every hour during the day, but in the morning he already ha $1,250 in the register. What is the expression that represents the total amount of money that he should have in the register in a given hour?A: $1250B: 6xC: 6x + 1250D: 1250x + 6 What is force and motion Les touristes vont ____ htel. A) de l Ils parlent _____ hpital. B) l Nous rentrons ____ cinma. C) du Why was the Proclamation of 1763 a cause of the American Revolution? Using complete sentences, identify and describe the events that took place in Germany after World War I and led to World War ll. From 9:00 p.m. to 6:00 a.m., the temperature dropped 1.6 degrees Fahrenheit per hour. What was the total change in temperature, in degrees Fahrenheit, between 9:00 p.m. and 6:00 a.m.? Which of the following substances increases in amount during the cellular respiration of glucose? Select one:a. O2b. NADHc. ADPd. Glucose ATP is used by theorgansmusclesentire body A car sharing service offers a membership plan with a $50 per month fee that includes 10 hours of driving each month and charges $9 for each additional hour (A) Write a piecewise definition of the cost F(x) for a month in which a member uses a car for x hours (B) Graph F(x) for 0 < x s 15 (C) Find lim x--->10 F(x), lim x--->10F(x), and lim x--->10F(x), which- ever exist. (a) At a simple interest rate of 12% per year, determine how long it will take $5000 to increase to twice as much. (b) Compare the time it will take to double if the rate is 20% per year simple interest. block of mass m sits at rest on a rough inclined ramp that makes an angle with the horizontal. What must be true about normal force F on the block due to the ramp