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
Korvikt [17]
3 years ago
11

A circle is translated 4 units to the right and then reflected over the x-axis. Complete the statement so that it will always be

true of the circle at the new location.
Mathematics
1 answer:
irga5000 [103]3 years ago
4 0

Answer:

The statement is now presented as:

\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}

In other words, this mathematical statement can be translated as:

<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>

Step-by-step explanation:

Let C = (h,k) the coordinates of the center of the circle, which must be transformed into C'=(h', k') by operations of translation and reflection. From Analytical Geometry we understand that circles are represented by the following equation:

(x-h)^{2}+(y-k)^{2} = r^{2}

Where r is the radius of the circle, which remains unchanged in every operation.

Now we proceed to describe the series of operations:

1) <em>Center of the circle is translated 4 units to the right</em> (+x direction):

C''(x,y) = C(x, y) + U(x,y) (Eq. 1)

Where U(x,y) is the translation vector, dimensionless.

If we know that C(x, y) = (h,k) and U(x,y) = (4, 0), then:

C''(x,y) = (h,k)+(4,0)

C''(x,y) =(h+4,k)

2) <em>Reflection over the x-axis</em>:

C'(x,y) = O(x,y) - [C''(x,y)-O(x,y)] (Eq. 2)

Where O(x,y) is the reflection point, dimensionless.

If we know that O(x,y) = (h+4,0) and C''(x,y) =(h+4,k), the new point is:

C'(x,y) = (h+4,0)-[(h+4,k)-(h+4,0)]

C'(x,y) = (h+4, 0)-(0,k)

C'(x,y) = (h+4, -k)

And thus, h' = h+4 and k' = -k. The statement is now presented as:

\exists\, (h,k)\in \mathbb{R}^{2} /f: (x-h^{2})+(y-k)^{2}=r^{2}\implies f': [x-(h+4)]^{2}+[y-(-k)]^{2} = r^{2}

In other words, this mathematical statement can be translated as:

<em>There is a point (h, k) in the set of real ordered pairs so that a circumference centered at (h,k) and with a radius r implies a equivalent circumference centered at (h+4,-k) and with a radius r. </em>

<em />

You might be interested in
A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
lozanna [386]
10 cents becuase you just - it

5 0
3 years ago
Read 2 more answers
Make r the subject of the formula t=r/r-3
trapecia [35]

Answer:

r = t(r-3)

Step-by-step explanation:

t = r/r-3

r/r-3 = t

r = t x (r-3)

6 0
3 years ago
This is an isosceles trapezoid.<br> R.<br> s<br> 75<br> X<br> Y У<br> T<br> U
LekaFEV [45]

Answer:

S=R

75+75=150

360-150=210

210/2=105

y=105

5 0
3 years ago
Read 2 more answers
PLEASE SOMEONE HELP WITH THESE 2 questions ASAP!! Will give double the points
zalisa [80]
The answer is
2)40
3)y=3\2
5 0
3 years ago
Write a number that is the same when rounded to the nearest hundred and ten
inn [45]
202 because you can round it to 200
7 0
3 years ago
Other questions:
  • Jessica just bought a refrigerator for $799. She paid $79.80 in a down payment and will pay the rest in 4 equal installments. Ho
    8·1 answer
  • What is the value of x in the equation 3x-4y=65 when y =4
    8·1 answer
  • What is the value of x?
    10·1 answer
  • Devin has a collection of 40 model vehicles which consists of 25 different cars and 15 different trucks. He selects 8 to display
    12·1 answer
  • A parking lot is 272.5 feet long and 151.25 feet wide. How much longer is the lot than it is wide?
    14·2 answers
  • Round to the nearest whole dollar: $9.49
    9·1 answer
  • The answer is 4,6,7
    11·1 answer
  • Jake biked 24 miles in 4 hours. If he biked at a constant rate of speed, how far did he bike in 1 hour?​
    11·2 answers
  • WILL MARK BRAINLYIST <br> what is the top length of the missing piece
    6·1 answer
  • - A statistical question is answered by a distribution of results.<br> ?<br> True or false
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!