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
scZoUnD [109]
3 years ago
9

Which describes how square S could be transformed to square S prime in two steps? Assume that the center of dilation is the orig

in. On a coordinate plane, square S has points (0, 0), (5, 0), (5, negative 5), (0, negative 5). Square S prime has points (0, 1), (0, 3), (2, 3), (2, 1). a dilation by a scale factor of Two-fifths and then a translation of 3 units up a dilation by a scale factor of Two-fifths and then a reflection across the x-axis a dilation by a scale factor of Five-halves and then a translation of 3 units up a dilation by a scale factor of Five-halves and then a reflection across the x-axis
Mathematics
1 answer:
gayaneshka [121]3 years ago
7 1

Answer:

The correct option is;

A dilation by a scale factor of Two-fifths and then a translation of 3 units up

Step-by-step explanation:

Given that the coordinates of the vertices of square S are

(0, 0), (5, 0), (5, -5), (0, -5)

Given that the coordinates of the vertices of square S' are

(0, 1), (0, 3), (2, 3), (2, 1)

We have;

Length of side, s, for square S is s = √((y₂ - y₁)² + (x₂ - x₁)²)

Where;

(x₁, y₁) and (x₂, y₂) are the coordinates of two consecutive vertices

When (x₁, y₁) = (0, 0) and (x₂, y₂) = (5, 0), we have;

s = √((y₂ - y₁)² + (x₂ - x₁)²) = s₁ = √((0 - 0)² + (5 - 0)²) = √(5)² = 5

For square S', where (x₁, y₁) = (0, 1) and (x₂, y₂) = (0, 3)

Length of side, s₂, for square S' is s₂ = √((3 - 1)² + (0 - 0)²) = √(2)² = 2

Therefore;

The transformation of square S to S' involves a dilation of s₂/s₁ = 2/5

The after the dilation (about the origin),  the coordinates of S becomes;

(0, 0) transformed to (remains at) (0, 0) ....center of dilation

(5, 0) transformed to (5×2/5, 0) = (2, 0)

(5, -5) transformed to (2, -2)

(0, -5) transformed to (0, -2)

Comparison of (0, 0), (2, 0), (2, -2), (0, -2) and (0, 1), (0, 3), (2, 3), (2, 1) shows that the orientation is the same;

For (0, 0), (2, 0), (2, -2), (0, -2) we have;

(0, 0), (2, 0) the same y-values, (∴parallel to the x-axis)

(2, -2), (0, -2) the same y-values, (∴parallel to the x-axis)

For (0, 1), (0, 3), (2, 3), (2, 1) we have;

(0, 3), (2, 3) the same y-values, (∴parallel to the x-axis)

(0, 1), (2, 1) the same y-values, (∴parallel to the x-axis)

Therefore, the lowermost point closest to the y-axis in (0, 0), (2, 0), (2, -2), (0, -2) which is (0, -2) is translated to the lowermost point closest to the y-axis in (0, 1), (0, 3), (2, 3), (2, 1) which is (0, 1)

That is (0, -2) is translated to (0, 1) which shows that the translation is T((0 - 0), (1 - (-2)) = T(0, 3) or 3 units up

The correct option is therefore a dilation by a scale factor of Two-fifths and then a translation of 3 units up.

You might be interested in
Two trains leave the same station at the same time, but are headed in opposite directions. One train travels at 70 mph and the o
Dmitry_Shevchenko [17]
If the required difference is 600 mi, lets start of counting by 10s and multiplying the current number
800-700 = 100
1600-1400 = 200
2400-2100 = 300
3200-2800 = 400
4000-3500 = 500
4800-4200 = 600
if 60 hours pass, they will be 600 miles away from each other.
counting by 10 each time will help with problems like or similar to this.

7 0
3 years ago
Read 2 more answers
An art teacher has a jar containing b buttons to distribute to her class for a project. In order to give each in the class 6 but
Nastasia [14]

Answer:

22

Step-by-step explanation:

Given:

An art teacher has the total number of buttons = b

1. In order to give each in the class 6 buttons, she will need 18 more buttons.

2. If she gives each child 5 buttons, she will have 4 left over.

Question asked:

How many children are in the class ?

Solution:

<u>Let total number of children in the class = </u>x

<u><em>As given that, 18 more buttons will be needed to give 6 buttons to each.</em></u>

The equation will be:-

b+18=6x\\b-6x=-18\ (equation\ 1)

<em><u>Also given that, If she gives 5 buttons to each, she will have 4 left over.</u></em>

The equation will be:-

b-5x=4\ (equation\ 2)

Subtraction equation 2 from 1

b-6x-(b-5x)=-18-4\\b-6x-b+5x=-22\\-6x+5x=-22\\-x=-22\\Minus\ canceled\ by\ minus\\x=22

Hence, total number of children are 22.

4 0
3 years ago
Find the measure of angle x in the figure below<br><br>A.35°<br>B.47°<br>C.51°<br>D.62°
Dafna11 [192]
First of all, we know that a line is 180°. This means if we add the angles of 61°, 57°, and angle y, we should get 180<span>°.

\sf 61\textdegree +57\textdegree+y=180\textdegree

Simplify:

\sf 118\textdegree +y=180\textdegree

Subtract 118° to both sides:

\sf y=62\textdegree

We also know that all three angles of a triangle add up to 180<span>°. So we have:

\sf 67\textdegree+62\textdegree +x=180\textdegree

Simplify:

\sf 129\textdegree +x=180\textdegree

Subtract 129° to both sides:

\sf x=\boxed{\sf 51\textdegree}
</span></span>
5 0
3 years ago
Read 2 more answers
If shoes are $20 each and the markup is 150%, how much will that cost?
MArishka [77]
<span>150% to decimal = 1.50 since 100% = 1 
</span><span>1.50 x 20 = 30
</span><span>30 + 20 = 50</span>
3 0
3 years ago
7.Find the lengths of the missing sides in the triangle. If your answer is not an integer, leave it in simplest radical form. Th
Fed [463]

Here a right angled triangle given. one angle with measure 45^o given. The three sides of the triangle given 4, x, y.

We have to find, the sides which is opposite, adjacent and hypotenuse here.

We know that the side opposite to right angle is always hypotenuse. So, hypotenuyse = y.

The side adjacent to the given angle 45^o is x. So, here adjacent = x.

The opposite side is opposite to the given angle. So, opposite = 4.

Now we will use SOHCAHTOA that is sin(x) =\frac{Opposite}{Hypotenuse} , cos(x) =\frac{Adjacent}{Hypotenuse} , tan(x) =\frac{Opposite}{Adjacent}, where x is the angle given.

To get x, we will use tan. So we will get,

tan(45^o) = \frac{4}{x}

We know the value of tan(45^o) = 1. By substituting the value we will get,

1 =\frac{4}{x}

To find x, we have to move x here to the left side by multiplying it to both sides. We will get,

(1)(x) = (\frac{4}{x}) (x)

x = 4

So we have got the value of x here.

Now to find y, we will use the trigonometric function sine.

sin(45^o) =\frac{4}{y}

we know the value of sin(45^o) =\frac{\sqrt{2}}{2}

By substituting the value we will get,

\frac{\sqrt{2}}{2}  = \frac{4}{y}

By cross multiplying we will get,

(\sqrt{2}) (y) = (4)(2)

\sqrt{2}y = 8

We will get y by dividing both sides by \sqrt{2}, we will get,

\frac{\sqrt{2}y}{\sqrt{2}}   =\frac{8}{\sqrt{2} }

y =\frac{8}{\sqrt{2}  }

Now we will rationalize the denominator by multiplying \sqrt{2} to the top and bottom.

y =\frac{8\sqrt{2}}{(\sqrt{2})(\sqrt{2})}

y =\frac{8\sqrt{2}}{2}

y = 4\sqrt{2}

So we have got the required values of x and y.

8 0
3 years ago
Read 2 more answers
Other questions:
  • the mendez family just bought a home for 180,000 if the value of the home increases at a rate of 3% per year, use an exponential
    8·1 answer
  • Help with this math question please
    12·1 answer
  • C (5,4) and D (3,10) find the length
    6·2 answers
  • What is the intercept of y+3=1/2x and y=5x-7x+8
    14·1 answer
  • What is the solution to the inequality below?<br> X^2&gt;=81
    15·1 answer
  • Using the frequency table given, find the mean, median, and mode.
    6·1 answer
  • The surface of a pool table has a perimeter of 26 feet and an area of 36 square feet. What are the dimensions of the pool table?
    14·1 answer
  • What is the range of the first graph &amp; the domain of the second graph ?
    7·2 answers
  • Find the measurement of angle JGH. *
    12·2 answers
  • Write an<br> explicit formula for an, the nth term of the sequence 112, 28, 7, ....
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!