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
For what values of x is the inequality 2/3 + x/3 >1 true?
Travka [436]

Answer:

B

Step-by-step explanation:

\frac{2}{3} + \frac{x}{3} > 1 ( multiply through by 3 to clear the fractions )

2 + x > 3 ( subtract 2 from both sides )

x > 1

6 0
2 years ago
What 5.871 5.781 is equal or lest or greater
RideAnS [48]
5.871 is greater than 5.781 because in the tenths place 8 is greater than 7. Also if you round the numbers to the nearest tenth, you get 5.9 versus 5.8
7 0
3 years ago
Read 2 more answers
I have 3 hundreds ,17 tens, 13 ones ,1 tenths, and 2 hundredths. What number am I?
Ksenya-84 [330]
=3*100 + 17*10 + 13*1 + 1*0.1 + 2*0.01
=300 + 170 + 13 + 0.1 + 0.02
= 483.12
(:
4 0
3 years ago
Please help do not answer if u don't know it
AveGali [126]

Answer:

the answer is D

Step-by-step explanation:

3 0
3 years ago
What is the percent of games won if a team won 92 games and lost 58 games?
Lera25 [3.4K]

Answer: 59.38%

there is the answer

5 0
2 years ago
Read 2 more answers
Other questions:
  • Which expression is the factorization of x² + 10x + 21?
    9·1 answer
  • Lisa, an experience shipping clerk, can fill a certain order in 10 hours. Bill, a new clerk, needs 13 hours to do the same job.
    9·1 answer
  • Marisol is cutting a 13.5-foot plece of ribbon for a craft project. She cuts off 4.5 feet,
    7·1 answer
  • Solve the inequality. Graph the solution.<br> 7z&lt; -28
    7·1 answer
  • If a cone has a radius of 2 cm and a height of 10 cm, what is the volume?
    11·2 answers
  • 1+1=21+1=21+1=21+1=21+1=21+1=21+1=21+1=21+1=21+1=21+1=2<br><br><br> lol
    15·2 answers
  • PLZZZZZZZZZZZZZZZZZ HELP!
    14·1 answer
  • How do I solve this inequality?
    5·1 answer
  • Last question for Jim Thompson Geometry homework
    11·1 answer
  • Show me how to do this on paper i need it right now
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!