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
Masja [62]
3 years ago
11

Triangle QRS is dilated according to the rule DO,2 (x,y). On a coordinate plane, (0, 0) is the center of dilation. Triangle Q R

S has points (negative 3, 3), (2, 4), and (negative 1, 1). What is true about the image ΔQ'R'S'? Select three options. Which statements are true? DO,2 (x,y) = (2x, 2y) Side Q'S' lies on a line with a slope of -1. QR is longer than Q'R'. The vertices of the image are closer to the origin than those of the pre-image. The distance from Q' to the origin is twice the distance from Q to the origin.

Mathematics
2 answers:
Xelga [282]3 years ago
6 0

Answer:

Options A, B and E are correct

Step-by-step explanation:

From the information given above, we would draw a dilation that produces an image that is the same shape as the original image, but has a different size.

The scale factor is 2

QRS → Q'R'S' = (x,y) → 2(x,y)

The coordinates of ∆QRS

Q (-3, 3)

R (2, 4)

S (-1, 1)

To get the coordinates of Q'R'S', we would multiply each coordinate of the original triangle by the scale factor of 2 since the dilation is from the origin. In order words, each vertex of QRS is multiplied by 2 to get each of the vertex of Q'R'S'.

2 (x,y) = (2x, 2y)

The coordinates of ∆Q'R'S' becomes:

Q' (-6, 6)

R' (4, 8)

S' (-2, 2)

To determine the statements that are true about the image ΔQ'R'S,

we would graph the coordinates of the two triangles.

Starting with ΔABC, we would draw the dilation image of the triangle with a center at the origin and a scale factor of 2.

See attached the diagram for better explanation.

Let's check out each options and compare it with diagram we obtained:

a) DO, 2 (x,y) = (2x, 2y)

A dilation about the origin with a scale factor 2 is described using the above notation.

Q' = 2(-3,3) = [2(-3), 2(3)] = (-6, 6)

R' (4, 8) = 2(2,4) = [2(2), 2(4)] = (4, 8)

S' (-2, 2) = 2(-1,1) = [2(-1), 2(1)] = (-2, 2)

This option is correct

b) Side Q'S' lies on a line with a slope of -1

Q' (-6, 6)

S' (-2, 2)

coordinate (x, y)

Slope = m = (change in y)/(change in x)

m = (6-2)/[-6-(-2)]

= 4/(-6+2) = 4/-4

m = -1

This option is correct

c) QR is longer than Q'R'

Length of QR (-3 to 2) = 5

Length of Q'R' (-6 to 4) = 10

QR is not longer than Q'R'

This option is false

d) The vertices of the image are closer to the origin than those of the pre-image

The scale factor determines how much bigger or smaller the dilation image will be compared to the preimage. In a transformation, the final figure is referred to as the image. The original figure is referred to as the preimage.

From the diagram, the vertices of the preimage (original image) are closer to the origin than those of the dilation image.

This option is false

e) The distance from Q' to the origin is twice the distance from Q to the origin.

The distance from Q' to the origin (6 to 0) = 6

The distance from Q to the origin (3 to 0) = 3

The distance from Q' to the origin = 2(the distance from Q to the origin)

This option is correct

JulijaS [17]3 years ago
6 0

Answer:

A,B and E is correct

Step-by-step explanation:

You might be interested in
Will surveyed students at his school about whether they have ever gone snowboarding and whether they own a skateboard. He found
larisa [96]

Answer:

third graph

Step-by-step explanation:

We represent the above information in a two way frequency table.


                             Have Snowboarded         Never Snawboarded          Total

Skateboard                          35                                     64                          99


No Skateboard                    13                                     147                        160


Total                                     48                                     211                        259


Therefore, the third graph is the correct answer.

6 0
3 years ago
Read 2 more answers
2. Find the<br> slope of the<br> line between<br> (8, 6) and<br> (20, -14)
Natalka [10]

Answer:

slopee = 5/3

Step-by-step explanation:

The  slope of a line is defined by the rise (the change in y-value) divided by the run (the change in x-value).  Here, the change in y-value is 6 - (-14) = 6 + 14 = 20.  The change in x-value is 20 - 8 = 12.  Therefore, the slope is 20/12 or (simplified) 5/3.

3 0
3 years ago
En el experimento Extraer una carta de una baraja española se consideran estos sucesos: A= 《Salir as 》 B= 《salir bastos 》 Calcul
Ganezh [65]

Answer:

They are compatible

Step-by-step explanation:

The first thing is to say that an "ace" and that it is a "coarse"

"ace" is card number 1. Group A

"coarse" is a type of the deck, found from number 1 to card 13. Group B

Thus:

 Calculate A U B:

1 to 13 + 1 of the other types of cards in the deck.

At intersection B:

1 of "coarse"

Therefore, if group A is compatible with group B

7 0
3 years ago
Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!!!!!!
AlexFokin [52]

Answer:

AE = 60 units

Step-by-step explanation:

GE is one third the length of AE so...

GE = 1/3(AE)

20 = 1/3x

3(20) = (1/3x)3/1

60 = x

x = 60

AE = 60 units

7 0
3 years ago
Based on Pythagorean identities, which equation is true? A. Sin^2 theta -1= cos^2 theta B. Sec^2 theta-tan^2 theta= -1 C. -cos^2
Arturiano [62]

Answer:

D

Step-by-step explanation:

our basic Pythagorean identity is cos²(x) + sin²(x) = 1

we can derive the 2 other using the listed above.

1. (cos²(x) + sin²(x))/cos²(x) = 1/cos²(x)

1 + tan²(x) = sec²(x)

2.(cos²(x) + sin²(x))/sin²(x) = 1/sin²(x)

cot²(x) + 1 = csc²(x)

A. sin^2 theta -1= cos^2 theta

this is false

cos²(x) + sin²(x) = 1

isolating cos²(x)

cos²(x) = 1-sin²(x), not equal to sin²(x)-1

B. Sec^2 theta-tan^2 theta= -1

1 + tan²(x) = sec²(x)

sec²(x)-tan(x) = 1, not -1

false

C. -cos^2 theta-1= sin^2

cos²(x) + sin²(x) = 1

sin²(x) = 1-cos²(x), our 1 is positive not negative, so false

D. Cot^2 theta - csc^2 theta=-1

cot²(x) + 1 = csc²(x)

isolating 1

1 = csc²(x) - cot²(x)

multiplying both sides by -1

-1 = cot²(x) - csc²(x)

TRUE

3 0
3 years ago
Other questions:
  • A wheel has a radius of 28 cm. If it does 50 revolutions, what distance will it travel?
    5·1 answer
  • A car traveled five miles in six minutes.<br>What was its speed in miles per hour?​
    15·2 answers
  • Connor borrows $8,000 at a rate of 19% interest per year. What is the amount due at the end of 7 years if the interest is compou
    9·1 answer
  • Point A has an x coordinate of −2 and lies in a circle with a center at (0, 0) and a radius of 5. To the nearest tenth, what is
    6·1 answer
  • Come up with two additional solutions now that you have graphed the line. Justify your solution numerically. At least one of you
    6·1 answer
  • The Boyle family drove at an average speed of 60 miles per hour. They drove for 4 hours. How far did the Boyle family drive?
    8·1 answer
  • 4. Find a pair of irrational numbers whose product is an integer.
    7·2 answers
  • For problems 6-9, using the formula net Force<br> =<br> 6)<br> a=2 m/s2<br> 8 kg<br> F = m•a =
    7·2 answers
  • Giving free brainliest
    13·2 answers
  • jason and ben are coworkers five years ago jason was 2.5 times as old as ben if ben is 31 how old is jason]
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!