MATHEMATICS COLLEGE

Find the scale factor of the line segment dilation. AB: endpoints (-6, -3) and (-3,-9) to A'B': endpoints at (-2, -1) and (-1, -3). A) -1/3 B) 1/3 C) 3D) -3

Answers

Answer 1

Answer:

we know that the endpoints of AB are

$\begin{gathered} (x_1,y_1)=\mleft(-6,-3\mright) \n (x_2,y_2)=(-3,-9) \end{gathered}$

and the distance formula is given by

$d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}$

By substituying these points, we have that

$d=\sqrt[]{(-3-(-6))^2+(-9-(-3))^2}$

which is equal to

$\begin{gathered} d=\sqrt[]{(-3+6)^2+(-9+3)^2} \n d=\sqrt[]{3^2+(-6)^2} \end{gathered}$

then

$\begin{gathered} d=\sqrt[]{9+36} \n d=\sqrt[]{45} \n d=\sqrt[]{9\cdot5} \n d=\sqrt[]{9}\cdot\sqrt[]{5} \n d=3\sqrt[]{5}\ldots..(A) \end{gathered}$

On the other hand, if

$\begin{gathered} (x_1,y_1)=(-2,-1) \n (x_2,y_2)=(-1,-3) \end{gathered}$

similarly to the previous case, the distance between the endpoint for A'B' is

$d=\sqrt[]{(-1-(-2))^2+(-3-(-1))^2}$

which is equal to

$\begin{gathered} d=\sqrt[]{(-1+2)^2+(-3+1)^2} \n d=\sqrt[]{1^2+(-2)^2} \n d=\sqrt[]{1+4} \n d=\sqrt[]{5}\ldots..(B) \end{gathered}$

Now, by comparing equation A and equation B, we can see that, the scale factor is 1/3.

Then, the answer is B.

Related Questions

A researcher records the repair cost for 8 randomly selected refrigerators. A sample mean of $57.89 and standard deviation of $23.69 are subsequently computed. Determine the 95% confidence interval for the mean repair cost for the refrigerators. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
...........................
Give brianliest and 15 points
5 Which situation can be modeled by Diagram A andwhich can be modeled by Diagram B?Diagram A:Whichadditionmodelssubtrac100% of x1096 10% 10% 10% 10% 1096 1096 1096 1096 109680% of x20% of xDiagram B:120% of10% 10% 1096 1096 10% 10% 10% 10% 10% 1096 10% 10%100% of x2096 of xa.Your bill at a restaurant is $68 and you want to leavea 20% tip. What is the total amount you will leave?b. You buy a sweater that is on sale for 20% off of theoriginal price. The sweater cost $28. What was theoriginal price?
A sample of 16 items from population 1 has a sample variance 5.8 and a sample of 21 items from population 2 has a sample variance 2.4. Test the following hypotheses at the .05 level of significance. H0: Population 1 Variance < Population 2 Variance Ha: Population 1 Variance > Population 2 Variance a. What is the p-value

QuestionAlice drove from the town of Everett to the town of Gage at an average speed of 45 miles per hour. If she
Grove for 40 minutes, how far did she travel? (1 hour = 60 minutes)

Answers

45 miles per hour is equal to 45 miles per 60 minutes. Let’s make it into a ratio, 45:60, and simplify it to 3:4 by dividing each by 15. Now, we can multiply the simplified ratio by 10 to get 30:40, which translates to 30 miles in 40 minutes.

Answer: 30 miles

5Type the correct answer in each box.
50°
60°
709
Х
50°
The value of xis
o, and the value of yis

Answers

Answer:

x = 60°

y = 50°

Step-by-step explanation:

✅x = 180° - (50° + 70°) (sum of interior angles of a triangle theorem)

x = 180° - 120°

x = 60°

✅Based on the exterior angle theorem, the sum of the opposite interior angles of a triangle = the exterior angle.

Therefore,

50° + 60° = x + y

Plug in the value of x

50° + 60° = 60° + y

110° = 60° + y

y = 110° - 60°

y = 50°

There are twenty classes at each of two middle schools. The number of students in each class at each school is shown in the dot plots below.Number of Students in Each Class at Poplar Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There are 3 dots above 20, 5 above 21, 7 above 22, 4 above 23, 1 above 24, and 0 above 25, 26, 27, 28, and 29.

Number of Students in Each Class at Oak Middle School
A dot plot. A number line going from 20 to 29 labeled Number of Students. There is 1 dot above 20, 2 above 21, 2 above 22, 4 above 23, 3 above 24, 2 above 25, 2 above 26, 2 above 27, 1 above 28, and 1 above 29.

Which statement correctly compares the mean number of students for the data in the plots?
There are about 2 more students in each class at Poplar Middle School than at Oak Middle School.
There are about 2 more students in each class at Oak Middle School than at Poplar Middle School.
There are about 5 more students in each class at Poplar Middle School than at Oak Middle School.
There are about 5 more students in each class at Oak Middle School than at Poplar Middle School.

Answers

The dot plot is missing, so i have attached it.

Answer:

B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

Step-by-step explanation:

From the dot plot attached, we can find the average number of students per class for each school.

For Poplar Middle School;

Total number of students = (20 × 3) + (21 × 5) + (22 × 7) + (23 × 4) + (24 × 1) = 435 students.

There are 20 classes.

Thus;

average number of students per class = 435/20 = 21.75

For Oak Middle School;

Total number of students = (20 × 1) + (21 × 2) + (22 × 2) + (23 × 4) + (24 × 3) + (25 × 2) + (26 × 2) + (27 × 2) + (28 × 1) + (29 × 1) = 483

Average number of students per class ; 483/20 = 24.15

Difference in average = 24.15 - 21.75 = 2.40

This implies that there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

Answer:

da answer is B lesss goooo

Step-by-step explanation:

What number Could be added in the expression -4 -9 that the value of the expression is 0

Answers

Answer:

+13

Step-by-step explanation:

-4-9 gives -13

when +13 is added to -13 , the expression becomes +13+(-13) =13-13=0

if i’m understanding this correctly -9 + -4 is equal to -13 so wouldn’t you just add 13 to make it 0?

sorry if this is confusing

Is -0.00992 a rational or irrational number?

Answers

Answer:

Yes, it is a rational number.

Step-by-step explanation:

You're Welcome :)

Answer is rational numer

40hrs $11.00/hr15%
8%
7%
What were each tax totals. What is the gross pay. What is the net pay. Show your work

Answers

Answer:

$440
$66, $35.20, $30.80
$308

Step-by-step explanation:

Gross pay means the amount of money you get without any tax reductions.

40 * 11 = $440

Find the value of all the taxes.

440 * 0.15 = $66

440 * 0.08 = $35.20

440 * 0.07 = $30.80

Net pay means the amount of money you get with tax reductions.

440 - 66 - 35.20 - 30.80 = $308

Best of Luck!

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