1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Phantasy [73]
3 years ago
11

How would you represent a rotation of 360 algebraically?

Mathematics
2 answers:
SSSSS [86.1K]3 years ago
5 0

Answer:

(x,y)(x,-y)

Step-by-step explanation:

ALGEBRAIC REPRESENTATIONS OF ROTATIONS

To rotate a figure in the coordinate plane, rotate each of its vertices. Then connect the vertices to form the image.

We can use the rules shown in the table for changing the signs of the coordinates after a reflection about the origin.

Example 1 :

The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 90° counterclockwise about the origin.

Solution :

Step 1 :

Trace triangle XYZ and the x- and y-axes onto a piece of paper.

Step 2 :

Let X', Y' and Z' be the vertices of the rotated figure.

Since the triangle is rotated 90° counterclockwise about the origin, the rule is

(x, y) ------> (-y, x)

Step 3 :

X(0, 0) ------> X'(0, 0)

Y(2, 0) ------> Y'(0, 2)

Z(2, 4) ------> Z'(-4, 2)

Step 4 :

Sketch the image X'Y'Z' using the points X'(0, 0),  Y'(0, 2) and  Z'(-4, 2).

Example 2 :

The triangle PQR has the following vertices P(0, 0), Q(-2, 3) and R(2,3). Rotate the triangle PQR 90° clockwise about the origin.

Solution :

Step 1 :

Trace triangle PQR and the x- and y-axes onto a piece of paper.

Step 2 :

Let P', Q' and R' be the vertices of the rotated figure.

Since the triangle is rotated 90° clockwise about the origin, the rule is

(x, y) ------> (y, -x)

Step 3 :

P(0, 0) ------> P'(0, 0)

Q(-2, 3) ------> Q'(3, 2)

R(2, 3) ------> R'(3, -2)

Step 4 :

Sketch the image P'Q'R' using the points P'(0, 0),  Q'(3, 2) and  Z'(3, -2).

Example 3 :

A quadrilateral has the following vertices A(0, 0), B(1, 2), C(4, 2) and D(3, 0). Rotate the quadrilateral 180° clockwise about the origin.

Solution :

Step 1 :

Trace the quadrilateral ABCD and the x- and y-axes onto a piece of paper.

Step 2 :

Let A', B', C' and D' be the vertices of the rotated figure.

Since the quadrilateral is rotated 180° clockwise about the origin, the rule is

(x, y) ------> (-x, -y)

Step 3 :

A(0, 0) ------> A'(0, 0)

B(1, 2) ------> B'(-1, -2)

C(4, 2) ------> C'(-4, -2)

D(3, 0) ------> D'(-3, 0)

Step 4 :

Sketch the image A'B'C'D' using the points A'(0, 0), B'(-1, -2), C(-4, -2) and  D'(-3, 0).

Example 4 :

The triangle XYZ has the following vertices X(0, 0), Y(2, 0) and Z(2, 4). Rotate the triangle XYZ 270° counterclockwise about the origin.

Solution :

Step 1 :

Trace triangle XYZ and the x- and y-axes onto a piece of paper.

Step 2 :

Let X", Y" and Z" be the vertices of the rotated figure.

Since the triangle is rotated 270° counterclockwise about the origin, the rule is

(x, y) ------> (y, -x)

Step 3 :

X(0, 0) ------> X"(0, 0)

Y(2, 0) ------> Y"(0, -2)

Z(2, 4) ------> Z"(4, -2)

Step 4 :

Sketch the image X"Y"Z" using the points X"(0, 0),  Y"(0, -2) and  Z"(4, -2).

Home page

9th

GenaCL600 [577]3 years ago
3 0

Answer:It means turning around until you point in the same direction again. Other ways of saying it: "Doing a 360" means spinning around completely once (spinning around twice is a "720").

...

A full rotation is 360 degrees.

Step-by-step explanation:

You might be interested in
Write an inequality for the graph
Liula [17]
Answer is d
yup
yup yup
8 0
3 years ago
Read 2 more answers
The volume of a sphere is 36π cubic feet. What is the radius of the sphere? (V = 4 3 πr3)
MrRa [10]

radius = 3 feet

rearrange the formula making r the subject

\frac{4}{3} πr³ = V ( multiply both sides by 3 to eliminate fraction )

4πr³ = 3V ( divide both sides by 4π )

r³ = \frac{3V}{4\pi } = ( 3 × 36π ) / 4π = 3 × 9 = 27

take the cube root of both sides

r = \sqrt[3]{27} = 3


6 0
3 years ago
The distance bewteen Harry and Kate is 2500 meters. Kate and Harry start walking toward one another and Kate' dog start running
Furkat [3]
Well, Kate and Harry together are walking 100 meters per minute. Which means it will take them 25 minutes to reach each other (I think). 

If the dog is running 120 meters per minute: 120 x 25 = 3,000.

The dog will run 3,000 meters (if he runs constantly to and from the spot that Kate and and Harry started).

4 0
3 years ago
HELP ASAP Linear Equations
Scilla [17]

Answer:

4th choice: I and IV only

Step-by-step explanation:

Change the form of the given equation to standard form.

y = -2/3 x + 2

3y = -2x + 6

2x + 3y = 6

Now compare this equation with the 4 choices.

Any equation that has the same x- and y-terms but a different constant term is parallel.

I. is parallel.

II. and III. are not parallel.

Look at IV.:

4x + 6y = 3

Divide both sides by 2:

2x + 3y = 3/2

IV. is also parallel.

Answer: 4th choice: I and IV only

4 0
3 years ago
Read 2 more answers
If you borrow $500 from a credit union at 12% annual interest and $250 from a bank at 18% annual interest, what is the effective
Gnesinka [82]

Answer:

B.  11.85% =  12%

Step-by-step explanation:      

500 * .10 + 300 * .15 = 50 + 45 = 95.

95/800 = .11875

.11875 = 11.875%

8 0
3 years ago
Read 2 more answers
Other questions:
  • Find an equation for the nth term of the arithmetic sequence.
    12·2 answers
  • PLEASE HELP ME FAST I NEED HELP
    13·1 answer
  • Cherries cost 4 dollars per pound. Mother bought r lbs and father bought 2 lbs. How much more money did mother spend on cherries
    13·2 answers
  • What is the value of x when x + 7 = 21? HElp if do so you get 20 ponits
    12·2 answers
  • TWO MINUTES HURRY HELP ME PLEASE
    11·2 answers
  • Dantes cell phone company charges $45 per month for unlimited calls and internet use and $0.25 per text message his last fell ph
    11·1 answer
  • How many 1/4can go in 1/8
    13·2 answers
  • What is 9 plus 10? Meme 123
    15·2 answers
  • I NEED HELP FAST PLEASE!
    7·1 answer
  • The formula F=9/5C+32 shows how to convert degrees Celsius, C to degrees
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!