The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,2)
What are the coordinates of Point C'? C'(__,__)
What are the coordinates of Point A? A(___,____)
Answers
Given:
The scale factor is [tex]s=\dfrac{1}{3}[/tex] and the center of dilation is at the point (4,2).
Red is original figure and green is dilated figure.
To find:
The coordinates of point C' and point A.
Solution:
Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
[tex](x,y)\to (k(x-a)+a,k(y-b)+b)[/tex]
According to the given information, the scale factor is [tex]\dfrac{1}{3}[/tex] and the center of dilation is at (4,2).
[tex](x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)[/tex] ...(i)
Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using (i), we get
[tex]C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)[/tex]
[tex]C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)[/tex]
[tex]C(-2,11)\to C'(-2+4,3+2)[/tex]
[tex]C(-2,11)\to C'(2,5)[/tex]
Therefore, the coordinates of Point C' are C'(2,5).
We assumed that point A is A(m,n).
Using (i), we get
[tex]A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)[/tex]
From the given figure it is clear that the image of point A is (8,4).
[tex]A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)[/tex]
On comparing both sides, we get
[tex]\dfrac{1}{3}(m-4)+4=8[/tex]
[tex]\dfrac{1}{3}(m-4)=8-4[/tex]
[tex](m-4)=3(4)[/tex]
[tex]m=12+4[/tex]
[tex]m=16[/tex]
And,
[tex]\dfrac{1}{3}(n-2)+2=4[/tex]
[tex]\dfrac{1}{3}(n-2)=4-2[/tex]
[tex](n-2)=3(2)[/tex]
[tex]n=6+2[/tex]
[tex]n=8[/tex]
Therefore, the coordinates of point A are (16,8).
Related Questions
A regular heptagon has sides measuring 26 mm and is divided into 7 congruent triangles. Each triangle has a height of 27 mm. What is the area of the heptagon?
Answers
Answer:
567 square mm
because 27*7 is 189 an times 3 because each side has 3 sides so it equals to 567 square mm! :)
Step-by-step explanation:
BRAINLIEST THAT BOOM!!!!!!!!!
If 13% is lost by selling goods for Rs 1475, what would be the loss or gain if the goods are sold for Rs 1615?
Answers
Given:
Loss percent is 13%.
Selling price = 1475
To find:
The loss or gain if the goods are sold for Rs.1615?
Solution:
Let x be the cost price of goods.
Loss percent is 13% and selling price is 1475.
[tex]1475=x-\dfrac{13}{100}x[/tex]
[tex]1475=x-0.13x[/tex]
[tex]1475=0.87x[/tex]
[tex]\dfrac{1475}{0.87}=x[/tex]
[tex]1695.4023=x[/tex]
[tex]x\approx 1695.40[/tex]
The cost price of goods is 1695.40.
We need to find the loss or gain if the goods are sold for Rs.1615.
Cost price is greater than the selling price because 1695.40 > 1615. It means , it is a loss.
[tex]Loss=CP-SP[/tex]
[tex]Loss=1695.40-1615[/tex]
[tex]Loss=80.40[/tex]
The loss percent is
[tex]Loss\%=\dfrac{Loss}{C.P}\times 100[/tex]
[tex]Loss\%=\dfrac{80.40}{1695.40}\times 100[/tex]
[tex]Loss\%\approx 4.74\%[/tex]
Therefore, the loss is 80.40 and the loss percent is about 4.74%.
Which answer represents the expression in its expanded form?
Answers
Multiplying by 0.51 is the same as decreasing by___%
Answers
Answer:
The correct answer is 51%
pls hurry will give brainliest
Answers
Answer:
Step-by-step explanation:
6(k + 2) + 1 = 13 (distribute 6 around the k+2)
6k + 12 + 1 = 13 (add 12 and 1)
6k + 13 = 13 (subtract 13 from both sides)
6k = 0 (divide by 6)
k = 0
Answer:
6( k + 2 ) + 1 = 13
6k + 12 + 1 = 13
6k + 13 = 13
6k = 0
k = 0/6
so it will 0
Mr. Starnes wondered what proportion of Katy Perry's Twitter followers are
female, so he selected a random sample of 500 of Katy Perry's followers. In the
sample, 308 are female. Construct and interpret a 90% confidence interval for the
true proportion of Katy Perry followers that are female.
Answers
Answer and Step-by-step explanation:
To calculate a confidence interval for a proportion:
1) Determine the proportion
[tex]p=\frac{308}{500}[/tex]
p = 0.616
2) A 90% confidence interval has z-score that is 1.645.
3) Calculate margin of error
[tex]ME=\sqrt{\frac{p(1-p)}{n} }[/tex]
where
n is the sample size
So
[tex]ME=\sqrt{\frac{0.616(1-0.616)}{500} }[/tex]
[tex]ME=\sqrt{\frac{0.616(0.384)}{500} }[/tex]
ME = 0.02175
Then the interval is given by
p ± z(ME)
0.62 ± 1.645(0.02175)
0.62 ± 0.035
The interval will be
0.585 < p < 0.655
What this means is that we are 90% confident that the true proportion of Katy Perry's Twitter female followers is between 0.585 and 0.655.
Amanda must read a 259−page book for her history class over the next week. Amanda has found that she can read 37 pages in a hour. Complete the table, select the appropriate graph, and enter an equation to represent the number of pages that Amanda has left to read with relation to time. Use variable x for hours.
Answers
Answer:
I dont have an answer but here is a example I hope it helps
Step-by-step explanation: Josie selected a number n. She divided n by 2 and then subtracted ½ from the result. She took
half of that result and then subtracted ½ to get the final result of 10. What is the value of n?
Let’s start by writing Josie’s first step as an expression. Dividing n by 2, then subtracting ½ from
the result would be (n/2) – ½. If we build on this expression with the information in Josie’s
second step, we get ½((n/2) – ½) – ½. Knowing the final result is 10, we can set up the equation
below, and solve for n as follows:
½((n/2) – ½) – ½ = 10
½(n/2) – ¼ - ½ = 10 (using the distributive property)
¼n – ¼ - ½ = 10 (multiplying to eliminate the parentheses)
¼n – ¾ = 10 (combining like terms)
¼n = 10¾ (adding ¾ to both sides of the equation)
n = 43 (dividing both sides of the equation by ¼)
30. Find the value of expression 20m2 + 30m + 40 when a)m = -3 b)m= - 4 c) m = 3
Answers
Answer:
di you mean m² when you say m2 or not?
The values of the expression are;
-21, 240, 310 respectively
We were given the equation as ;
20 [tex]m^{2}[/tex] + 30m + 40
Then we can find the values of the expression with the given options to know the answer by input the value of ' m' into the given equation
Option (a) (m=-3)20( [tex]-3^{2}[/tex] )+ 30(-3)+ 40 = -21Option (b) (m=-4)20([tex]-4^{2}[/tex] )+ 30(-4)+ 40 = 240Option (c) (m=3)20([tex]3^{2}[/tex]) + 30(3)+ 40 = 310Therefore, the values of the expression are; -21, 240, 310 respectively
Learn more at: https://brainly.com/question/9585437?referrer=searchResults
Pls answer if u know the answer, don't just do it for points.
A motor is rated at 1500 Watts and a second motor is rated at 2200 Watts. If they each needed to lift a 100 kg box 20 meters, which one would get the job done first?
Answers
Answer:
motor of the 1500
Step-by-step explanation:
i took the test hopefully is the right one.
James is building a doll house that is proportional to his own house. He is using a scale of 0.5 inch = 1 foot. If the doll house is 12.3 inches tall, how tall is his house?
Answers
3n + 8 = 53
I don’t understand how to find the n
Answers
Answer:
n=15
Step-by-step explanation:
subtract 8 from both sides to get 3n=45
divide both sides by 3 to solve for n to get n=15
Answer:
n = 15
Step-by-step explanation:
3n + 8 = 53
the first step we are going to do is combine the like terms by moving the constant (8) to the right and subtracting
3n = 45
next step, we are going to isolate the n by dividing by 3 on both sides of the equation
3n divided by 3 is just n and 45 divided by 3 is 15, so we have our answer
LAST QUESTION!!! ANSWER THIS QUESTION PLZZZZ
Answers
Answer:
A. 80 yardsStep-by-step explanation:
Corresponding sides have same ratio in similar figures:
75/50 = 120/x x = 120*50/75x = 80Correct option is A
E.C. What is the standard equation of a circle with center (h,k) and radius r in the coordinate plane?
Answers
Answer:
(x-h)^2 + (y-k)^2 = r^2
Step-by-step explanation:
Here, we want to write the standard equation of the circle
We have this as;
(x-h)^2 + (y-k)^2 = r^2
The above equation is the standard equation for the circle
Answer:
(x − 4)2 + (y + 6)2 = 25
(x − 4)2 + (y − (-6))2 = 52
When I compare my equation with the standard form, (x − h)2 + (y − k)2 = r2, I get h = 4, k = -6, and r = 5. The center is at (4, -6), and the length of the radius is 5.
Step-by-step explanation:
edmentum
whats is the cost of electricity to run personal computer
Answers
Answer: Desktop computers can cost anywhere from $300-$4,000 depending on how good it's inside components are. The average computer might go for around $400. For more advanced computers the price might be $1,000 or more. All in all, the cost of a computer / PC truly depends on how much power you're needing from it.
Step-by-step explanation:
Srry its kinda confusing but I hope it helped
Answer:
We estimate that an average modern desktop PC will use approximately 100 watts of power, not including the display screen. Click calculate to find the energy consumption of a desktop computer using 100 Watts for 6 hours a day with $0.10 per kWh
Step-by-step explanation:
If , then what is mto the nearest degree?
Answers
Answer:
70 degrees
Step-by-step explanation:
If cosm<A = 342/1000, we are to find the value of a
Take arccos of both sides
cosm<A = 342/1000
cosm<A = .342
arccos(cosm<A) = arccos(0.342)
m<A = arccos(0.342)
m<A = 70 degrees
Hence the measure of m<A is 70 degrees
for educational purposes which is better vans or nike?
Answers
PLEASE HELP ME I BEGGGGGGG
Answers
Answer:
A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
I believe it is A because according to the theorem it states the other pair of opposite sides are parallel.
"Here's the game plan. Assume that ¯BC ¯AD and ¯BC ~= ¯AD. By definition, a parallelogram is a quadrilateral with both pairs of opposite sides parallel. You already know that one pair of opposite sides is parallel. You need to show that the other pair of opposite sides is parallel. In other words, you need to show that ¯AB ¯CD."
Megan ran 1 3/4 miles. What is this as an improper fraction?
Answers
Answer:
Yes it is improper fraction
Add the polynomials:
2a+3b+5a-7b Explain your response
Answers
7a - 4b
Step-by-step explanation:
Add the numbers ending with 'a' together, and then add the numbers ending with 'b' together.
First of all, I will put the letters beside each other.
2a + 5a + 3b - 7b
2a + 5a = 7a
3b - 7b = - 4b
Therefore, the answer is 7a - 4b.
x^{2}-3x-40=0x
2
−3x−40=0
Answers
Answer:
what the
Step-by-step explanation:
what is that weird
Annual snowfall in Anchorage, Alaska, is normally distributed with a mean height of 76 inches and a standard deviation of 4.7 inches. What is the probability this year that it will snow between 71.4 and 80.7 inches in Anchorage?
Answers
Using the Empirical Rule, it is found that there is a 68% probability this year that it will snow between 71.4 and 80.7 inches in Anchorage.
What is the Empirical Rule?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.In this problem, the mean height of 76 inches and a standard deviation of 4.7 inches, hence 71.4 and 80.7 inches is within 1 standard deviation of the mean, that is, there is a 68% probability this year that it will snow between 71.4 and 80.7 inches in Anchorage.
To learn more about the Empirical Rule, you can take a look at https://brainly.com/question/24537145
3 pencils cost $0.45. What is the cost per pencil?
Answers
Answer:
0.15
Step-by-step explanation:
The solution (x y) to a system of equatiohs is the point where they..?
Answers
Answer:
Intersect
Step-by-step explanation:
ayuda por favor 5.800%(-10)
Answers
Answer: -0.58
Divide 5.8 y 100 y te da 0.058 despues lo multiplicas con (-10) y te da -0.58
Sketch the graph of each linear inequality
Answers
Given the triangle information below solve for the x value and the measure in degrees of angle a
Answers
x+x=2x
61+43+90=194
2x+194=180
194-189
2x=15
x=7.5
43+7.5=50.5
Tony made a scale drawing of his living room. The scale drawing has a length of 5 inches and a width of 3 inches. If the living room has an actual length of 12 feet, which equation could be used to determine w, the width of the living room?
Answers
Answer:5w=36
Step-by-step explanation:
Dom runs a pizza business. Last year he took in $88 000 and it cost him $33 000
to run. What is his percentage profit for the year? Round to the nearest cent.
Answers
Answer:
The percentage profit for the year is 62.50%
Step-by-step explanation:
Here, we want to calculate the percentage profit
That would be difference between the revenue (88,000) and the cost (33,000) divided by the revenue * 100%
We have this as;
(88,000-33,000)/88,000 * 100%
= 55,000/88,000 * 100%
= 62.50%
Anyone know how to do this?!!
Answers
Answer:
slope is -1/4
Step-by-step explanation:
[tex]\frac{-4}{12}[/tex]=[tex]\frac{-1}{4}[/tex]
[tex]\frac{-2}{8}[/tex]= [tex]\frac{-1}{4}[/tex]
and so on...
formula: [tex]\frac{x}{y}[/tex]
hope this helps!!!
5 donuts and 2 cups of hot Chocolate costs 24$. 2 donuts and 3 cups of hot chocolate costs 14$.How much does each donut and each cup of hot chocolate cost
Answers
Answer:cost of each donut =$4
and cost of each cup of hot chocolate =$2
Step-by-step explanation:
Step 1
Let donuts be represented as d
and cups of hot chocolate be rep as c so that
5 donuts and 2 cups of hot Chocolate costing 24$ will be expressed as
5 d+ 2 c= 24
And 2 donuts and 3 cups of hot chocolate costing 14$ will be expressed as
2d +3 c= 14
Step 2
Using elimination method,Multiply equation 1 by 3 and equation 2 by 2
15d+ 6c= 72----equation 3
4d+ 6c= 28-----equation 4
Subtracting equation 4 from equation 3 gives us
11 d=44
d= 44/11
d= 4
To find c, using equation 1
5 d+ 2 c= 24
5 x 4+ 2c=24
20+2c=24
2c=24-20
2c=4
c=4/2 =2
cost of each donut =$4
and cost of each cup of hot chocolate =$2