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
koban [17]
3 years ago
12

The green triangle is a dilation of the red triangle with a scale factor of s=1/3 and the center of dilation is at the point (4,

2)
What are the coordinates of Point C'? C'(__,__)

What are the coordinates of Point A? A(___,____)

Mathematics
1 answer:
klasskru [66]3 years ago
5 0

Given:

The scale factor is s=\dfrac{1}{3} and the center of dilation is at the point (4,2).

Red is original figure and green is dilated figure.

To find:

The coordinates of point C' and point A.

Solution:

Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

(x,y)\to (k(x-a)+a,k(y-b)+b)

According to the given information, the scale factor is \dfrac{1}{3} and the center of dilation is at (4,2).

(x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)            ...(i)

Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using (i), we get

C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)

C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)

C(-2,11)\to C'(-2+4,3+2)

C(-2,11)\to C'(2,5)

Therefore, the coordinates of Point C' are C'(2,5).

We assumed that point A is A(m,n).

Using (i), we get

A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)

From the given figure it is clear that the image of point A is (8,4).

A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)

On comparing both sides, we get

\dfrac{1}{3}(m-4)+4=8

\dfrac{1}{3}(m-4)=8-4

(m-4)=3(4)

m=12+4

m=16

And,

\dfrac{1}{3}(n-2)+2=4

\dfrac{1}{3}(n-2)=4-2

(n-2)=3(2)

n=6+2

n=8

Therefore, the coordinates of point A are (16,8).

You might be interested in
Simplify 2(a-3)/(a-4)(a-5)+(a-1)/(3-a)(a-4)+(a-2)/(5-a)(a-3)​
Umnica [9.8K]

Answer:

  \dfrac{5}{x^3-12x^2+47x-60}

Step-by-step explanation:

Though it is not what you have written, we think you want to simplify ...

  \dfrac{2(a-3)}{(a-4)(a-5)}+\dfrac{(a-1)}{(3-a)(a-4)}+\dfrac{(a-2)}{(5-a)(a-3)}\\\\=\dfrac{2(a-3)^2}{(a-3)(a-4)(a-5)}+\dfrac{-(a-1)(a-5)}{(a-3)(a-4)(a-5)}+\dfrac{-(a-2)(a-4)}{(a-3)(a-4)(a-5)}\\\\=\dfrac{2(a^2-6a+9)-(a^2-6a+5)-(a^2-6a+8)}{x^3-12x^2+47x-60}\\\\=\boxed{\dfrac{5}{x^3-12x^2+47x-60}}

_____

When writing a fraction in plain text, parentheses are needed around the entire denominator. The order of operations tells you that a/bc = (a/b)c, not a/(bc).

6 0
2 years ago
Which rational number equals 0 point 5 with bar over 5? 1 over 50 1 over 5 5 over 10 5 over 9
kolbaska11 [484]

Answer is b or the second option

Step-by-step explanation:

7 0
3 years ago
Find the radius of convergence, r, of the series. ∞ xn 2n − 1 n = 1 r = 1 find the interval, i, of convergence of the series. (e
Bingel [31]
Assuming the series is

\displaystyle\sum_{n\ge1}\frac{x^n}{2n-1}

The series will converge if

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|

We have

\displaystyle\lim_{n\to\infty}\left|\frac{\frac{x^{n+1}}{2(n+1)-1}}{\frac{x^n}{2n-1}}\right|=|x|\lim_{n\to\infty}\frac{\frac1{2n+1}}{\frac1{2n-1}}=|x|-\lim_{n\to\infty}\frac{2n-1}{2n+1}=|x|

So the series will certainly converge if -1, but we also need to check the endpoints of the interval.

If x=1, then the series is a scaled harmonic series, which we know diverges.

On the other hand, if x=-1, by the alternating series test we can show that the series converges, since

\left|\dfrac{(-1)^n}{2n-1}\right|=\dfrac1{2n-1}\to0

and is strictly decreasing.

So, the interval of convergence for the series is -1\le x.
6 0
3 years ago
What is the value of the expression shown below? 7 + (2 + 6) 2 ÷ 4 ⋅ 1 over 2 whole to the power of 4 and explain.
ValentinkaMS [17]

The answer is B.







....................................

6 0
3 years ago
Read 2 more answers
An international company has 27,200employees in one country. If this represents
Mariana [72]
23.2% of the total employees is 27,200

0.232x = 27,200
x = 27,200 / 0.232
x = 117,241 (thats rounded) <==
6 0
3 years ago
Other questions:
  • Refer to this question below Thank You.
    13·1 answer
  • To find a reciprocal of a fraction, switch the numerator and denominator.
    5·1 answer
  • 6/16 equals 8 over what?
    10·2 answers
  • Factorise 6x^2 - 21x
    5·1 answer
  • Solve for y, y-8= -( y-2) / 2
    12·2 answers
  • Which rectangular prism will have the largest volume
    14·1 answer
  • What is the volume of the rectangular prism
    8·1 answer
  • -3y+15 2y+4<br> _____ = ______<br> 6 7
    9·1 answer
  • Whai si (3x+5) (x-2)
    6·1 answer
  • Please show work on how to simplify this 1/x^-3/6 <br> Thank you in advance
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!