Describe each of the following transformation that maps the figures described below. Be specific by naming lines of reflection, centers of rotation and degrees of rotation, distance and direction of translations, and centers of dilation with a scale factor. Determine if the transformation is a rigid transformation or a similarity transformation. Explain all reasoning.
Part A: Figure 1 →Figure 4
Part B: Figure 2 → Figure 5
Answers
Answer:
Part A: Figure 1 → Figure 4
Rigid Transformation
Equivalent to a reflection about the origin, or a rotation of 180° clockwise or anticlockwise about the origin which are types of rigid transformation
Part B: Figure 2 → Figure 5
Similarity transformation
Figure 5 is Figure 2 dilated by a scale factor of 1/2, which is a form of a similarity transformation
Step-by-step explanation:
Part A: Figure 1 → Figure 4
The coordinates of the vertices of the preimage are;
(5, 10), (2, 4), (9, 2)
The coordinates of the vertices of the image are;
(-9, -2), (-2, -4), (-5, -10)
Which is equivalent to a reflection about the origin, or a rotation of 180° clockwise or anticlockwise about the origin
Part B: Figure 2 → Figure 5
The coordinate points of figure 2 are;
(-9, 2), (-5, 10), and (-2, 4)
The coordinate points of figure 5 are;
(1, 2), (2.5, -1), and (4.5, 3)
The lengths of the sides of figure 2 are;
√((10 - 2)² + ((-5) - (-9))²) = 4·√5
√((10 - 4)² + ((-5) - (-2))²) = 3·√5
√((2 - 4)² + ((-9) - (-2))²) = √53
The lengths of the sides of figure 5 are;
√(((-1) - 2)² + (2.5 - 1)²) = (3·√5)/2
√((4.5 - 2.5)² + (3 - (-1))²) = 2·√5
√((4.5 - 1)² + (3 - 2)²) = (√53)/2
Therefore. Figure 5 is Figure 2 dilated by a scale factor of 1/2
Therefore, given that the sides of Figure 2 and Figure 5 are rotated by 180°
We have;
Figure 5 is obtained as follows;
1) The rotation of figure 2 by 180°, clockwise or anticlockwise about the origin to get;
(-9, 2), (-5, 10), and (-2, 4) → (9, -2), (5, -10), and (2, -4)
2) The image is translated left by 1 blocks and up by 6 blocks as follows;
(9, -2), (5, -10), and (2, -4) → (8, 4), (4, -4), and (1, 2)
3) The image is then dilated by a scale factor of 1/2 with a center of dilation of (1, 2) to get;
Preimage (8, 4), (4, -4), and (1, 2) → Image (1, 2), (2.5, -1), and (4.5, 3).
Related Questions
What is the slope in the equation y=3/4x
What is the y-intercept also?
Answers
Answer:
slope = 3/4
y- intercept : (0,0)
Step-by-step explanation:
Understanding Elevation
Death Valley, Califomia, has an elevation of -282 feet What does this mean?
It is 282 feet above sea level
It is 282 feet below sea level.
It is - 282 feet above sea level
Itis - 282 feet below sea level
Answers
Answer:
Step-by-step explanation:
if it has a negative elevation of 282 feet than its below sea level by 282 feet if its 282 feet above with no negative than its 282 feet above sea level i hope this helped
Answer:
hi the answer is b)It is 282 feet below sea level.\
have a nice day!
Step-by-step explanation:
mark me brainliest?
3(6d - 24) = 6(12 + 3d)
pls solve i need
Answers
3D = 32 or D = (10 2/3)
Step-by-step explanation:
We want to make D only one side so we subtract 3D from the left
Then we slowly make the equation smaller and smaller by adding 24 to each side, multiplying the numbers, then finally getting our answers.
Answer:
No solutions
Step-by-step explanation:
Distribute the 3 to the first set of parentheses:
3(6d - 24) = 6(12 + 3d)
18d - 72 = 6(12 + 3d)
Distribute the 6 to the other set of parentheses:
18d - 72 = 72 + 18d
Subtract 18d from both sides:
-72 = 72
-72 [tex]\neq[/tex] 72
Since -72 and 72 are not equal, there are no solutions
Please help, please write a proof to prove the “prove” section
Answers
question 4 pleeeeease help
Answers
In a survey of 2,800 people who owned a certain type of car, 1,400 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answers
Answer:
50% of people would buy the car again.
Step-by-step explanation:
2800 divided by 2 is 1400.
The percent of the people surveyed were satisfied with the car is 50%.
Given that,
In a survey of 2,800 people who owned a certain type of car, 1,400 said they would buy that type of car again.Based on the above information, the calculation is as follows:
[tex]= 1400 \div 2800[/tex]
= 50%
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Exercise 1: Which of the following is not an equation
(1) 2x + 3 = 10
(2) 3+2 = 5
(3) 3(2x + 1)
(4) 1+ 4 = 10
Answers
Answer:
(3) 3(2x +1 )
Step-by-step explanation:
For (1), (2), and (4), all of them give an answer while (3) does not which means that (3) is not an equation.
the douglas family visits sealand and is charged $72.00 for 2 adults and 3 child tickets. the williams family also visited sealand and was charged $78.00 for 1 adult and 5 child tickets. how much would it cost the lopez family to go to sealand if they have 3 adults and 4 children
Answers
2a + 3c = 72
1a + 5c = 78 you need to get one of them the same so do 1a +5c=78 x2 =
2a + 10c = 156 , then 2a + 10c = 156 subtract 2a +3c= 72 which is 7c = 84 divide by 7 each side so c = 12 so a child ticket is £12 then so the same for the adults so 2a +3c= 72 x 5 = 10a + 15c =360 then do 1a + 5c = 78 x3 = 3a + 15c= 234 then 10a + 15c =360 subtract 3a + 15 c= 234 = 7a = 126 then divide by 7 each side so a = 18 so an adults ticket is £18
Then do 18 + 18 + 18 + 12 + 12 + 12 + 12 = 102 so it would cost the Lopez family £102 to go to sea-land
hope this makes sense .
Question 1
Find an expression equivalent to 8(2x+1)(x-2)(x+3)
Answers
Answer:
18x + 13
Step-by-step explanation:
just add like terms after multiplying 2x + 1 by 8
16x + 8
x - 2
x + 3
18x + 13
What is the 4th equivalent fraction to 1/8
Answers
Answer:
2/16
Step-by-step explanation:
this is the 4th equivalent fraction to 1/8
Eli's Diner sold 50 milkshakes last week. 60% of the milkshakes had whipped cream on top. How many milkshakes with whipped cream were sold?
Answers
Answer:
30 will be the number of milkshakes had whipped cream on top.
Step-by-step explanation:
Total number of milkshakes sold by Eli's Diner last week = 50
As 60% of the milkshakes had whipped cream on top.
Let x be the number of the milkshakes had whipped cream on top.
[tex]x=\frac{60}{100}\times 50[/tex]
[tex]x=\frac{60}{2}[/tex]
[tex]x=30[/tex]
Therefore, 30 will be the number of milkshakes had whipped cream on top.
15% off of $60, then subtracting 10% from that cost, is equal to
Answers
Answer:
8.1 i think
Step-by-step explanation:
say hi and i will mark brainllyist or whatever
Answers
Answer:
hi hows your day
Step-by-step
Of the following, which is the solution to 2x2 + 3x = −5?
Answers
Answer:
Step-by-step explanation:
Nothing to choose from??/
But 2x^2+3x=-5 is
- 3± i√31 / 4
Answer:
[tex]\frac{-3+-i\sqrt{31} }{4}[/tex]
ye
Which of the following points would be on the graph of the equation y=−4x+6?(−4, −10)(−4, 22)(1, −10)(1, −2)
Answers
Answer:
Only the point (-4, 22) is ON THE GRAPH of the equation. Please also check the attached graph.
Step-by-step explanation:
Given the equation
[tex]y=-4x+6[/tex]
Let us substitute all the given points to check which points satisfy the equation.
Substitute (-4, -10) in the equation
[tex]y=-4x+6[/tex]
[tex]-10=-4(-4)+6[/tex]
[tex]-10=16+6[/tex]
[tex]-10=22[/tex]
As the R.H.S ≠ L.H.S, hence (-4, -10) does not satisfy the equation.
Hence, (-4, -10) is NOT ON THE GRAPH of the equation
Substitute (-4, 22) in the equation
[tex]y=-4x+6[/tex]
[tex]22 = -4(-4)+6[/tex]
[tex]22 = 16+6[/tex]
[tex]22 = 22[/tex]
As the R.H.S = L.H.S, hence (-4, 22) satisfies the equation.
Hence, (-4, 22) is ON THE GRAPH of the equation. Please also check the attached graph.
Substitute (1, -10) in the equation
[tex]y=-4x+6[/tex]
[tex]-10=-4(1)+6[/tex]
[tex]-10=-4+6[/tex]
[tex]-10=2[/tex]
As the R.H.S ≠ L.H.S, hence (1, -10) does not satisfy the equation.
Hence, (1, -10) is NOT ON THE GRAPH of the equation
Substitute (1, -2) in the equation
[tex]y=-4x+6[/tex]
-2 = -4(1)+6
-2 = -4 + 6
-2 = 2
As the R.H.S ≠ L.H.S, hence (1, -2) does not satisfy the equation.
Hence, (1, -2) is NOT ON THE GRAPH of the equation
Therefore, from the above analysis, we conclude that only the point (-4, 22) is ON THE GRAPH of the equation. Please also check the attached graph.
Inside an auditorium, 1 out of 5 people wear hats, and 4 out of 5 people do not wear hats. Based on this information, predict how many wear hats if there are 215 people.
Answers
Answer:
43
Step-by-step explanation:
2-\dfrac12n=3n+162− 2 1 n=3n+16
Answers
Answer:
2-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+162-\dfrac12n=3n+162− 2 1 n=3n+16
Step-by-step explanation:
May I have brainliest please? :)
Haley spent 1/2 hour playing on her cell phone that use 1/9 of her battery how long does she have to play on her phone to use the entire battery?
Answers
Answer:
4 1/2 hours.
Step-by-step explanation:
If 1/2 an hour only used up 1/9 of her battery, 9, 1/2 would give us 9/2, which if you simplified it gets you 8 1/2 hours. Hope this helps! Have a great day!
Sixth grade Y.14 Factor using th
Factor 10y + 20z.
Answers
Answer:
17zy
Step-by-step explanation:
big brain
Answer:
y+z=30
Step-by-step explanation:
y=10 z=20
y+z=30
(-3, 8) is a solution to the following system of equations: 4x + 3y = 12 5x + 2y = 1 True False
Answers
Answer: True
Step-by-step explanation:
Shawn said that in standard notation,
7.142 x 107 will have 7 zeros after the
2 because the exponent is a 7. Is he
correct? Why or why not?
Answers
Answer:
Shawn is incorrect.
Step-by-step explanation:
The decimal is moving 7 places to the right. The 2 is the third digit, so there will be 4 0s after it.
Find k such that the roots of the quadratic are real, rational, and equal: 9x^2+kx+1=0
Answers
Answer:
Step-by-step explanation:
9x^2+kx+1=0
k= -9x-1/x
Which number goes in the box?
8 + 9 = 9 +
Answers
Answer:
8
Step-by-step explanation:
I hope this helps you out!
Answer:
8
Step-by-step explanation:
...
Which of the following graphs represents the equation above -3x+2y=8
Answers
Answer:
Is there a picture of the graphs...?
Step-by-step explanation:
Anyways, the answer should be y= 3/2x +4
If you show me the graphs I could possibly help you find which one is correct.
Answer:
Step-by-step explanation:
Here are the graphs, which one goes with
y = 4 + 3/2x ?
Is the sequence arithmetic? If yes, determine the common difference. *
(1 Point)
-14-9, -4, 1, 6, ...
O no, it does not increase or decrease the exact same amount
O yes, d = 5
O yes, d = -5
Answers
Answer:
Option 2: Yes, d= 5 is the correct answer
Step-by-step explanation:
An arithmetic sequence is a sequence where the common difference between the consecutive terms is same.
Given arithmetic sequence is:
-14, -9, -4, 1, 6
To check if it is an arithmetic sequence, we have to find the common difference d
[tex]a_1 = -14\\a_2 = -9\\a_3 = -4\\a_4 = 1[/tex]
Now,
[tex]d = a_2-a_1 = -9-(-14) = -9+14 = 5\\d = a_3 - a_2=-4-(-9) = -4+9 = 5\\d = a_4-a_3 = 1-(-4) = 1+4 = 5[/tex]
As the common difference is same, the given sequence is an arithmetic sequence.
Hence,
Option 2: Yes, d= 5 is the correct answer
Pt.2 Please show your work
Find the slope when given the following points
(-3, 2) and (1, 0)
Answers
Answer:
slope is = -1/2
Step-by-step explanation:
y2-y1= 2-0= 2
x2-x1= -3-1= -4
2/-4= -1/2
m=___
x-x
it would be 2-0 OVER (fraction formula shown above) -3-1
so your end fraction would be 2/-4 which would be -0.5
so, your slope would be -0.5
PLEASE HELP!!
You need to factor by grouping.
Please explain the steps!
Answers
Answer:
3(k-4)(7k^2+5)
Step-by-step explanation:
1) Factor out GCF
3(7k^3-28k^2+5k-20)
2)Split into two
3) Factor
3*7k^2(k-4)+5(k-4)
3(k-4)(7k^2+5)
A deal is a deal, so here is a good one, let's see who gets it right. I had $10.00. My mom gives me $30.00, My dad gave me $30.00. My aunt and uncle give $100.00. I had another $10.00. How much money did I have?
Answers
Answer:
$180 in total!
Step-by-step explanation:
10 + 30 + 30 + 100 + 10 = 180
the uncle and aunt gave their money together, it didn't specify that they each gave 100
Answer:
The total amount of money i have is $180.
Step-by-step explanation:
Given information:
The money i have = $10
Mom gives = $30
Dad gives = $30
Aunt and uncle gives = $100
Now i had another $10
The total amount of money (x) i have is the sum of all money i receive.
x = 10+30+30+100+10
x = 180
Hence , the total amount of money i have is $180.
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Tao wants to check that the expression 3(4x – 6) simplifies to 12x – 18. What is the value when 2 is substituted for x into both expressions? The value of each expression is 2. The value of each expression is 6. The value of one expression is 2, and the value of the other expression is 6. The value of one expression is 6, and the value of the other expression is –6.
Answers
Answer:
The value of each expression is 6.
Step-by-step explanation:
3 * 4 = 12 and 3 * 6 = 18
So 3(4x - 6) = 12x - 18
12(2) - 18 = 24 - 18 = 6
Answer:
the value of each expression is 6
Step-by-step explanation:
edge 2020
Aanya got 5 marks in Science test. Her friend Sneha got 'x' marks more than Aanya. How many marks did they get altogether?
Pls Answer FAST