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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:

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João claims he can read minds. His friend Pedro asked him to guess a number he was thinking of between 1 and 7 (inclusive). João
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It can be deduced that the probability of having 4 or more correct guesses will be 0.0296.

<h3>How to calculate the probability</h3>

From the given information, the null hypothesis is p = 1/7 and the alternate hypothesis is p>1/7. In this case, the mind reader gets a 4 out of 9 chances.

In order to test the hypothesis, simulations for 10000 cases were run with a probability of the correct answer being 1/7.

In this case, the p-value is the probability of correct answers that are greater than 4, assuming the null hypothesis is true. Here the p-value is 0.0296.

Also, the significance level to reject the hypothesis is less than 0.01. Since p > 0.01, we then fail to reject the hypothesis. Therefore the null hypothesis stands and Joao is not a mind reader.

Learn more about probability on:

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2 years ago
Chiara purchased a new natural gas barbecue for $2,100 and made a down payment that was 30% of the purchase price. She financed
Svetllana [295]

Answer: Chiara's monthly payment is $194.7

Step-by-step explanation:

The cost of the new natural gas barbecue for $2,100. She made a down payment 30% off the purchase price. This means that the amount of down payment made is

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Amount left to pay would be

2100 - 630 = $1470

The formula for determining monthly loan payment is

A = P(r(1 + r)^n)/((1 + r)^n - 1)

There would be 9 monthly payments, so

n = 9

r = 0.055/12 = 0.0046

P = 1470

A = 1470(0.0046(1 + 0.0046)^9)/((1 + 0.0046)^9 - 1)

A = (1470 × 0.0049)/0.037

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3 years ago
The perimeter of a rectangle is 56 cm. When its length is reduced by 2 cm and its
Svetlanka [38]
187 cm squared.

Based on rectangle:

2L + 2W = 56

Draw the square and name your sides the following:
(W+4) , (L-2), (W+4), (L-2)

Because it’s a square, all sides are equal and we can remove and solve for one of the variables but keep in mind the parameter changed..

The new parameter is 56 minus 4cm + 8cm...keep in mind I used 4cm and 8cm because we have a 2 Lengths and 2 Widths.

Solving 60= 4 (w+4)
W= 11

So the side of our square is 11+4=15

L-2 = 15
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So the area of the Rectangle is 11*17=187 cm squared.

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Solve for e: 7 e - 4 = 31
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