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
Joe is moving out of his apartment. The elevator can carry, at most, 2500 poundsHe has identical boxes that are each 40 pounds. If Joe weighs 160 pounds, how many boxes can he put on the elevator ?
Answers
Answer:
58
Step-by-step explanation:
first we want to write an equation and that equation would be
2500=40x+160 now we solve for x
step 1 subtract 160 from each side
2340=40x
then we divide each side by 40
x=58.5
because he cant bring half a box he can only bring 58
Ill give u branliest if u help plsss
The graphs of f (x) and g() are shown.
Answers
Answer:
the Answer is 2 hope that helps
I need help yall. Brainliest for the first person who actually shows their work.
30 pts btw
Answers
Answer:
1. 24.36
2. Do the same thing (follow the steps in the picture)
Step-by-step explanation:
Maria was approved for a 10-year, Federal Unsubsidized student loan in the
amount of $17,700 at a rate of 3.9%. Loan repayment will begin after 4.5
years.
Answers
Answer:
3796.65
Step-by-step explanation:
I = $ 3,106.35
Equation:
I = Prt
Calculation:
First, converting R percent to r a decimal
r = R/100 = 3.9%/100 = 0.039 per year,
then, solving our equation
I = 17700 × 0.039 × 4.5 = 3106.35
I = $ 3,106.35
The simple interest accumulated
on a principal of $ 17,700.00
at a rate of 3.9% per year
for 4.5 years is $ 3,106.35.
$ 6,903.00 - 3,106.35 = 3796.65
Please answer correctly !!!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!
Answers
Answer:
TWU is congruent to WUV
(I actually don't know if that's how I'm supposed to answer it but do what you will)
Determine the relationship between the two triangles and whether or not they can be
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The two triangles are related by
, so the triangles
Answers
Answer:
congruent by side angle side so the triangle is congruent
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Answers
Answer:
[tex]2^{9}[/tex]
Step-by-step explanation:
Using the rule of exponents
[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
note that 8 = 2³ and so
8³ = (2³ )³ = [tex]2^{3(3)}[/tex] = [tex]2^{9}[/tex]
State a number that would lie between -2.15 and -2.16 on the number line
Answers
2.151, 2.152, 2.153, 2.154, 2.155, 2.156, 2.157, 2.158, 2.159
there are more possibilities, but these are the most simple answers you could give :) hope this helped!
A number that would lie between -2.15 and -2.16 on the number line are 2.151.
What is a number line?Integers are arranged at equal intervals along horizontal straight lines called number lines. A number line can be used to represent every number in a series. The endpoints of this line go on forever. Some will have a defined beginning and end. It refers to those as closed number lines. Number lines might be alternatively left empty or blank. A number ladder is a vertical number line.
There are some possibilities would include the following:
2.151, 2.152, 2.153, 2.154, 2.155, 2.156, 2.157, 2.158, 2.159
therefore, the numbers that are between 2.15 and 2.16 are 2.151.
Learn more about number line here:
brainly.com/question/13425491
#SPJ2
Ivan is saving money to buy a game. So far he has saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
PLS HELP ME!
Answers
Answer:
36$
24/2*3=$36
Answer:
$18
Step-by-step explanation:
The game costs $24, and so far he has saved three- fourths of the cost.
3/4(24)=x
Renee and Thomas live at the beach and collect seashells. The number of shells Renee collects on any given day, R, is approximately Normal with a mean of 58.2 shells and a standard deviation of 12.8 shells. The number of shells Thomas collects on any given day, T, is approximately Normal with a mean of 47.9 shells and a standard deviation of 11.5 shells. Assume the two random variables are independent of each other. What is the probability that on a randomly selected day the total number of shells collected by Renee and Thomas is 120 or more? 0.002 0.209 0.284 0.791
Answers
Answer: .209
Step-by-step explanation:
took the test
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Answer:
-1/2
Step-by-step explanation:
Answer:
-1/2
Step-by-step explanation:
convert mixed fraction to impropoer fraction
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Answer:
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Answer:
an addition problem
Step-by-step explanation:
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Answers
Answer:
one side = 8xy²·[tex]\sqrt{2x}[/tex]
Step-by-step explanation:
if the area is 128x^3y^4 then to find one side you must take the square root
[tex]\sqrt{128}[/tex][tex]\sqrt{x^3}[/tex][tex]\sqrt{y^4}[/tex] = [tex]\sqrt{4}[/tex][tex]\sqrt{32}[/tex][tex]\sqrt{x^2}[/tex][tex]\sqrt{x}[/tex][tex]\sqrt{y^2}[/tex][tex]\sqrt{y^2}[/tex] =
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8xy²·[tex]\sqrt{2x}[/tex]
PlS HELP ME!!!!!!!!!!!!
Answers
9514 1404 393
Answer:
6. A
7. C
8. E
Step-by-step explanation:
6. Devon gets $0.45 for each of the s programs he sells, so his pay for selling is 0.45s. He gets a $40 flat rate for each game, so his total pay is ...
p = 0.45s + 40 . . . . . matches choice A
__
7. Robert gets $25 per hour in tips for each of the x hours he works, so his tip earnings are 25x. He gets a $40 flat rate for each day he works, so his total pay for working x hours is ...
y = 25x +40 . . . . . matches choice C
__
8. The graph of a proportional relationship is a straight line through the origin. This is described by B and C, so choice E is the best.
The value of Maggie's car decreased by 10% since last year, when she bought it. If the car is now worth $16,000.00, how much was the car worth when she bought it?
Answers
Answer: 17600
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Use the Distributive Property on 45x-6
Answers
Answer:
180Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
yes
Step-by-step explanation:
A restaurant wants to study how well its salads sell. The circle graph shows the sales over the past few days. If 35 of the salads sold were garden salads, how many total salads did the restaurant sell?
Answers
-The given is that they sold 35 garden salads which is 70% of their sales.
-Now, to get how many salads 1% is equal to, you divide 35 by 70
-35/70 = 0.5
-So now, multiply 16 by 0.5 and 14 by 0.5
-16(0.5)=8 and 14(0.5)=7
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70% of 50 is 35
16% of 50 is 8
14% of 50 is 7
Hope this helps and is right, have a good day!
HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP
Answers
Answer:
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Step-by-step explanation:
260 out of 300
300 our of 360
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A hollow metallic cylinder is made from a metallic sheet of 2.4 cm thickness. The inner
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step by step explain plz
Answers
Answer:
The volume of the metal used is 5277.9 cm³.
Step-by-step explanation:
The volume of a cylinder is given by:
[tex] V = \pi r^{2} h [/tex]
Where:
r: is the radius
h: is the height = 50 cm
The volume of metal ([tex]V_{m}[/tex]) can be found by subtracting the internal volume ([tex]V_{i}[/tex]) from the external volume ([tex]V_{e}[/tex]):
[tex] V_{m} = V_{e} - V_{i} [/tex]
[tex] V_{m} = \pi r_{e}^{2} h - \pi r_{i}^{2} h [/tex]
The external radius is given by the sum of the internal radius with the tickness:
[tex] r_{e} = t + r_{i} [/tex]
Hence, the volume is:
[tex] V_{m} = \pi*50 cm((2.4 cm + 5.8 cm)^{2} - (5.8 cm)^{2}) = 5277.9 cm^{3} [/tex]
Therefore, the volume of the metal used is 5277.9 cm³.
I hope it helps you!
Solve the following equation for X.
3x- 4 = 11
Answers
Answer: B
Step-by-step explanation:
3x - 4 = 11
add 4 to both sides so it cancels out
3x = 15
Now divide by 3
x = 5
Answer:
x=5
Step-by-step explanation:
3x - 4 = 11
4 + 11 = 15
3x = 15
x = 5
can u help me please
Answers
Answer:
xy=1.5
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Step-by-step explanation:
Members of a club are making tie-die t-shirts. They made 104 t-shirts in the first week and need to
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Answers
Answer:
34.3%
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Which answers flow, clockwise and counterclockwise, in the circular flow model of the economy?
money
natural resources
productivity
goods and services
Choose exactly two answers that are correct.
Answers
Answer:
goods and services
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Step-by-step explanation:
Answer:
The answer is A. Money and D. Goods and Services.
I took the test
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
1/2 is 50% So you add 19 and 50 to get 69% or 69/100
What is the sum of the interior angles of this pentagon? MULTIPLE CHOICE EASY
Answers
Answer:
Option B 540 is the amswer