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
satela [25.4K]
2 years ago
5

The point B(1, 1) is rotated 90° counterclockwise around the origin. What are the co

Mathematics
1 answer:
Thepotemich [5.8K]2 years ago
3 0

Given that the point B is (1,1) is rotate 90° counterclockwise around the origin.

We need to determine the coordinates of the resulting point B'.

<u>Coordinates of the point B':</u>

The general rule to rotate the point 90° counterclockwise around the origin is given by

(x, y) \rightarrow(-y, x)

The new coordinate can be determined by interchanging the coordinates of x and y and changing the sign of y.

Now, we shall determine the coordinates of the point B' by substituting (1,1) in the general rule.

Thus, we have;

Coordinates of B' = (1,1) \rightarrow(-1,1)

Thus, the coordinates of the resulting point B' is (-1,1)

You might be interested in
Translate to inequality twice a number is at most 40
kow [346]
In mathematical form, it would be: 2x ≥ 40
x ≥ 20

Hope this helps!
5 0
3 years ago
find the parametric equations for the line of intersection of the two planes z = x + y and 5x - y + 2z = 2. Use your equations t
Kaylis [27]

Answer:

You didn't give the points in which you want the parametric equations be filled, but I have obtained the parametric equations, and they are:

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

Step-by-step explanation:

If two planes intersect each other, the intersection will always be a line.

The vector equation for the line of intersection is given by

r = r_0 + tv

where r_0 is a point on the line and v is the vector result of the cross product of the normal vectors of the two planes.

The parametric equations for the line of intersection are given by

x = ax, y = by, and z = cz

where a, b and c are the coefficients from the vector equation

r = ai + bj + ck

To find the parametric equations for the line of intersection of the planes.

x + y - z = 0

5x - y + 2z = 2

We need to find the vector equation of the line of intersection. In order to get it, we’ll need to first find v, the cross product of the normal vectors of the given planes.

The normal vectors for the planes are:

For the plane x + y - z = 0, the normal vector is a⟨1, 1, -1⟩

For the plane 5x - y + 2z = 2, the normal vector is b⟨5, -1, 2⟩

The cross product of the normal vectors is

v = a × b =

|i j k|

|1 1 -1|

|5 -1 2|

= i(2 - 1) - j(2 + 5) + k(-1 - 5)

= i - 7j - 6k

v = ⟨1, -7, -6⟩

We also need a point on the line of intersection. To get it, we’ll use the equations of the given planes as a system of linear equations. If we set z = 0 in both equations, we get

x + y = 0

5x - y = 2

Adding these equations

5x + x + y - y = 2 + 0

6x = 2

x = 1/3

Substituting x = 1/3 back into

x + y = 0

y = -1/3

Putting these values together, the point on the line of intersection is

(1/3, -1/3, 0)

r_0= (1/3) i - (1/3) j + 0 k

r_0​​ = ⟨1/3, -1/3, 0⟩

Now we’ll plug v and r_0​​ into the vector equation.

r = r_0​​ + tv

r = (1/3)i - (1/3)j + 0k + t(i - 7j - 6k)

= (1/3 + t) i - (1/3 + 7t) j - 6t k

With the vector equation for the line of intersection in hand, we can find the parametric equations for the same line. Matching up r = ai + bj + ck with our vector equation,

r = (1/3 + t) i + (-1/3 - 7t) j + (-6t) k

a = (1/3 + t)

b = (-1/3 - 7t)

c = -6t

Therefore, the parametric equations for the line of intersection are

x = (1/3 + t)

y = (-1/3 - 7t)

z = -6t

3 0
3 years ago
What is 2(2x+1) equivalent to
Nostrana [21]
2(2x+1)= (2 x 2x) + (2 x 1) = 4x + 2
6 0
3 years ago
Read 2 more answers
A rectangle has a perimeter of 16 feet. What is a possible length and width for the rectangle? A rectangle has a perimeter of 16
matrenka [14]

Answer: width 2.5 length 4

Step-by-step explanation:

4 0
3 years ago
Which expression is equivalent to (sin x + 1)(sin x − 1)? A. cos2x B. -cos2x C. cos2x + 1 D. cos2x − 1 E. -cos2x + 1
Semenov [28]

ANSWER

B.

- \cos^{2} x

EXPLANATION

The given expression is

(sin x + 1)(sin x − 1)

Note that:

(x + 1)(x - 1) =  {x}^{2}  - 1

This implies that,

( \sin \: x + 1)( \sin \: x - 1)  =   \sin^{2} x - 1

We can factor -1 on the right hand side to get,

( \sin \: x + 1)( \sin \: x - 1)  =    - (1 - \sin^{2} x )

Note that from the Pythagorean Identity

1 - \sin^{2} x = \cos^{2} x

We apply this identity to obtain:

( \sin \: x + 1)( \sin \: x - 1)  = - \cos^{2} x

The correct choice is B

4 0
3 years ago
Other questions:
  • Find the next two terms in the given sequence, then write it in recursive form. A.) {7,12,17,22,27,...} B.) { 3,7,15,31,63,...}​
    13·1 answer
  • Simplify the following equation: (5 + 3)²​
    10·2 answers
  • Estimate 58% of 121 by using 10%. show work please​
    7·1 answer
  • Very confused on 1-3. please help
    14·1 answer
  • PLEASE HELP 50 POINTS!!! Jordan is constructing the bisector of MN
    8·2 answers
  • Tacoma's population in 2000 was about 200 thousand, and has been growing by about 8% each year. If this continues, what will Tac
    6·1 answer
  • Two trains leave stations 360 miles apart at the same time and travel toward each other. One train travels at 70 miles per hour
    11·2 answers
  • Express sinV as a fraction and as a decimal to the nearest hundredth
    9·1 answer
  • Help me solve this problem please
    6·1 answer
  • What is the value of x in the triangles to the right?<br> A. 9<br> B. 12<br> C. 15<br> D. 17.5
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!