What are the coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right?
Answers
The coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right are (8,9) (for clockwise rotation) and (0,-9) (for counterclockwise rotation)
How does rotation by 90 degrees changes coordinates of a point if rotation is with respect to origin?Let the point be having coordinates (x,y).
Case 1: If the point is in first quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 2: If the point is in second quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 3: If the point is in third quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 4: If the point is in fourth quadrant:Subcase: Clockwise rotation:
Then (x,y) → (y, -x)
Subcase: Counterclockwise rotation:
Then (x,y) → (-y, x)
Case 5: For points on axesYou can take that point in any of the two surrounding quadrants. Example, if the point is on positive x axis, then it can taken as of first quadrant or fourth quadrant.
Case 6: On originNo effect as we assumed rotation is being with respect to origin.
For this case, the point (-9,4) (present in second quadrant) is rotated by 90 degrees.
This rotation can be either clockwise, or counterclockwise.
Thus, for each case, we have:
case 1: Clockwise rotation:Then (x,y) → (y, -x), therefore, (-9,4) → (4, 9)
case 2: Counterclockwise rotation:Then (x,y) → (-y, x), therefore, (-9,4) → (-4, -9)
Now, when shifting to right by 4, that means, we're making no changes vertically, but old x-coordinates are increased by 4 to make them shift to right side as value of x increases as we go more and more to the right side with respect to the origin and in defaultly oriented cartesian space.
Thus, we have:
case 1: Clockwise rotation:
After translation of 4 units right:
(4, 9) → (4+4, 9) = (8,9)
case 2: Counterclockwise rotation:After translation of 4 units right:
(-4, -9) → (-4+4, -9) = (0,-9)
Thus, the coordinates of the point (-9, 4) after a 90 degree rotation followed by a translation 3 units right are (8,9) (for clockwise rotation) and (0,-9) (for counterclockwise rotation)
Learn more about rotation of a point with respect to origin here:
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Related Questions
Help me with this math plz
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vocabulary is a repeating decimal a rational number?
a. no because it cannot be written in form of a/b where a and b are intergers and b=0
b. no because it cannot be written in form a b where a and b are integers.
c. yes because it can be written in the form a/b where a and b are integers are b=0
d yes because it can written in the a.b where a and b integers.
Answers
if not d, it’s probably c, but the denominator for a repeating decimal (b) shouldnt always be 0, it could be 1. ex: .333/1
Yes, because it can be written in the form a/b where a and b are integers are b = 0. Then the correct option is C.
What is a rational number?If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.
The vocabulary is a repeating decimal a rational number will be given as,
Yes, because it can be written in the form a/b where a and b are integers are b = 0.
Then the correct option is C.
More about the rational number link is given below.
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Can you help this this question
40 points
Answers
Do you need this in a graph form?
Answer:
1. Equation 1
2. -2x-3(6x-11)=-7
3. x=2
4. y=1
5. (2,1)
Please do ASAP! Its not worth anything so please just do! Points, brainliest, thanks
Answers
Answer:
yes
Step-by-step explanation:
0.19 kg baseball moving at +26.80 m/s is slowed to a stop by a catcher who exerts a constant force of -371 N. How long does it take this force to get to the creator the answer is -8
A shelf has 4 blue pairs of pants, 2 black pairs of pants, 1 white pair of pants, and 3 tan pairs of pants. You randomly choose a pair of pants from the shelf. What is the probability of choosing a blue pair of pants as a percent? - the answer isn’t 60%.
Answers
Answer:
Probability can best be seen as the total number of “successful” outcomes (non blue pants) divided by the total number of possible outcomes (all pants). Normally, you express probability as a fraction (6/10), a ratio (6:10), or a percentage (60%). You could also express the probability as .6, or 6 out of 10.
My thought process: There are 4 pair of blue pants and 6 pair of non-blue pants. When you pick, you have 4 chances (pants) out of 10 chances (pants) of getting blue, and, therefore, 6 chances (pants) out of 10 chances (pants) of getting “not blue”. That is 60%; 6:10; 6/10; .6; or 6 out of 10.
I need help with number 4... ;-;
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Answer:
I picked C because it depends on the temperature that is being presented in the area. In a hotter area, a larger scale wind will be place. In a colder area a local wind would preferably be placed.
Answer:
All wind is caused by the uneven heating of the earth's surface, which sets convection currents in motion, convection currents on a large scale cause global winds: convection currents on a small scale cause local winds.
hope this helps!!:)
Step-by-step explanation:
.
3 x 2.5 =
2 x 3.4 =
Answers
Answer:
7.5
6.8
Step-by-step explanation:
hope it helped :-)
Answer:
7.5
6.8
Step-by-step explanation:
because 3x 2.5 is 7.5 and 2x3.4 is 6.8
Graph the description of each line A line has a slope of -3 and a y-intercept of 3.
Answers
Answer:
The equation is y = -3 + 3
Step-by-step explanation:
It will go through (0,3) and it wil go up 3 right one.
Answer:
equation: y= -3x+3
Step-by-step explanation:
Subustitute formula y=mx+b for the slope=m and in this case the slope is -3. and the y intercept=b so if u plug in m and b in the formula y=mx+b you get y=-3x+3. next, since the slope, put the -3 over 1 to create a fraction. next, plot the point (0,3) as the y-int. then follow the pattern -3 down right 1. So the points to plot are (0,3), (1,0) (2,-3)
Michael deposits $2650 into an account. The interest rate on the account is 6% compounded annually. What is the balance in Michael's account after 2 years? After 3 years?
Answers
Answer:
1 year would be 2809
Step-by-step explanation:
Answer:im late but 1 year would be 2809
Step-by-step explanation:
what is (16)^(0.25)⠀⠀⠀⠀⠀⠀⠀⠀
Answers
Answer:
the answer is 2
I hope this helped :)
Answer:
the correct answer is 2
just it
You pick a card at random.
6789
What is P(9)?
Answers
- i am assuming P(9) means probability of 9.
what we know:
there is only one 9 in the number.
there are 4 digits in total.
answer:
1/4
-- let me know if you have questions regarding this.
At a school health fair, individual pieces are places in paper bags and distributed to students randomly. There are 20 apples, 15 apricots, 25 bananas, 25 pears and 30 peaches. What is the probability of getting an apple?***Hint: Reduce
A. 19/23
B. 4/23
C. 20/100
D. 1/2
Answers
Answer:
B
Step-by-step explanation:
B)90/115 so the probability is 18/23
C)95/115 so the probability is 19/23
D) is impossible because there are no oranges
Find the slope of the line in the graph.
Answers
Answer: m = -2
Step-by-step explanation: To get from one point to the next along this line,
we must first go down 2 units so we say that our rise is -2.
From there we move 1 unit to the left so our run is 1.
So our slope or rise over run is -2/1 or -2.
Simplify the expression all the way down.
−5(1+2k)−8(−4+5k)
Question 1 options:
-50k+27
-30k+37
-5-10k+32-40k
32-5-40k
Answers
Answer:
-50k+27
Step-by-step explanation:
=(−5)(1)+(−5)(2k)+(−8)(−4)+(−8)(5k)
=−5+−10k+32+−40k
Combine Like Terms:
=−5+−10k+32+−40k
=(−10k+−40k)+(−5+32)
=−50k+27
In Mr. Quad’s PE class, 48 out of 50 students dressed out. Use one of the three forms of ratios to represents the ratio of students who did NOT dress out to the total number of students.
Answers
Answer:
2:50
Step-by-step explanation:
simple subtraction and then add the number of kids the other side of the ratio. 50 - 48 = 2 and there was 50 kids in total, so 2:50
mewooooooooooooooooooooo
Answers
Answer:
Step-by-step explanation:
2 5
4 10
8 15
10 25
i think lol
Ms. Li gave her students a quiz that was supposed to take 6 minutes to complete. She asked her students to record the amount of time, to the nearest minute, that it took them to complete the quiz. Ms. Li wants to create a data display that will summarize the data and show how many students took 6 minutes to complete the quiz. Which data display should she create?
A. a box plot
B. a dot plot
C. a histogram with intervals 1-3, 4-6, 7-9, and 10-12
D. a histogram with intervals 1-4, 5-8, and 9-12
Answers
Answer:
b
Step-by-step explanatits b
its b
I NEED YOUR HELP!!
The table shows input and output values of a function given a rule. Which function represents the rule?
Input: x, a number; Output: y, 3 less than 2 times x
Input,x -2 -1 0 1 2
Output,y -7 -5 -3 -1 1
A. Y= 2x - 3
B. Y= -2x + 3
C. Y= -3x - 2
D. Y= 3x + 2
Answers
Because 2 times x is 2x, and 3 less than that is -3. So we can write them into 2x - 3 = Y
The correct function for the given rule will be;
⇒ Y = 2x - 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Input: x, a number
Output: y, 3 less than 2 times x
And,
Input, x -2 -1 0 1 2
Output, y -7 -5 -3 -1 1
Now,
Since, For the function we have;
Input: x, a number
Output: y, 3 less than 2 times x
So, We get;
The function is,
⇒ Y = 2x - 3
And, Here given that;
Input, x -2 -1 0 1 2
Output, y -7 -5 -3 -1 1
Substitute all the values and check it as;
⇒ Y = 2x - 3
Put Y = - 7 , x = - 2
⇒ - 7 = 2 × - 2 - 3
⇒ - 7 = - 4 - 3
⇒ - 7 = - 7
Thus, The value of function is,
⇒ Y = 2x - 3
Learn more about the mathematical expression visit:
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help with this problem
Answers
Answer: X= -1/4
Hope it helps!
problem in the picture
Answers
Answer:
B)
Step-by-step explanation:
65 x 2.5 = 162.5
70 x 1.5 = 105
162.5+105=267.5
65 x 2.5=162.5
70x 1.5=105
105+162.5=267.5
Factor the following expression using the GCF: 42pr – 3p.
3p(14r)
p(42r – 3)
3p(14r – 1)
42p(r – 3)
Answers
Help PLZ I will give 15 points and brainliest!!!
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Please answer!!!!! I will give brainliest!
Answers
Which relation is a function
Answers
Answer:
Look at image posted.
Step-by-step explanation:
The one I circle would be the answer because there should not be 2 points for every x-axis value. The 1st one has 2 points with x=0, the other 2 also have 2 points on the asme x axis value
On a math test, 4 out of 20 students received an A. Two students are randomly selected without replacement, and the first student has an A. What is the probability of the second student having an A?
Answers
Answer:
Step-by-step explanation:
The answer should be 20% chance
Two students selected without replacement, and the first student and second student having is 16/95
Probability-based problem:What information do we have?
Number of total students = 20
Number of students having A = 4
Two students selected without replacement, and the first student has an A = 4/20 × 16/19
Two students selected without replacement, and the first student has an A = 64 / 380
Two students selected without replacement, and the first student has an A = 16 / 95
Probability of the second student having an A = 16/20 × 4/19
Probability of the second student having an A = 64 / 380
Probability of the second student having an A = 16 / 35
Find out more information about 'Probability'.
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The number of tourists at the beach per weekend in July was 55,000. In November, the number of tourists per weekend was 18,000. Find the percent of change from July to November. (Round to the nearest Thousands place)
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A company that makes hair-care products had 7,000 people try a new shampoo. Of the 7,000 people, 56 had a mild allergic reaction. What percent of the people had a mild allergic reaction?
Answers
Answer:
0.8%
Step-by-step explanation:
What is the relationship between the ratios? 10:14 and 30:36 Drag and drop to complete the statement. The ratios are (porportional, not porportional)
Answers
Answer:
Not Proportional
Step-by-step explanation:
30/10 = 3
36/14 = 2.57142857143
Answer:
The ratios are not proportional
Step-by-step explanation:
Can someone help me with this please? I don't know how to do it, and I need the answer asap ;-; (Image Below)
Answers
Answer:
ma'am or sir... there is no picture attached... but whats the question?
Step-by-step explanation:
Please help id appreciate it and please give me full answers. I will report.
Jane is training for a triathlon. After swimming a few laps, she leaves the health club and bikes 16 miles south. She then runs 12 miles west. Her trainer bikes from the health club to meet Jane at the end of her run.
How much farther does Jane travel than her trainer? Answer the questions to find out.
1. What is the total distance Jane travels biking and running? Include units with your answer.
2. Use the Pythagorean theorem to write an equation for the distance Jane's trainer bikes.
3. Solve your equation to find the distance Jane's trainer bikes. Show your work.
4. How much farther does Jane travel than her trainer?
Answers
Answer:
Part 1. 28 miles
Part 2. 16^2 + 12^2 = c^2
Part 3. 8 miles. All work is in step by step explanation.
Part 4. 8 miles
Step-by-step explanation:
Part 1. The total distance that Jane travels biking and running is 28 miles. This is because we add 16 and 12 which is her total route.
Part 2. The Pythagorean theorem is a^2 + b^2 = c ^2. In this case, the variable a is Jane's bike route(16 miles), the variable b is Jane's running route(12 miles), and the variable c is the Trainer's biking route as given. If we replace all variables with the values in miles, the equation would be 16^2 + 12^2 = c^2.
Part 3. WORK USED FROM EQUATION
16^2 = 16*16 = 256
12^2 = 12*12 = 144
Now we replace the numbers with the exponents with the solved numbers.
256 + 144 = c^2
256 + 144 = 400
400 = c^2
c = sqrt400
c = 20
Finally, we take the value of c and subtract it from the total distance of Jane's route which is 28 miles(as explained above).
28 - 20 = 8.
Hence, the answer is 8 miles