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
cricket20 [7]
3 years ago
9

PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al

l that apply. The length of side AD is 8 units. The length of side A'D' is 4 units. The image is larger than the pre-image. Sides CD and C'D' both have the same slope, 2. The scale factor is .

Mathematics
1 answer:
hichkok12 [17]3 years ago
6 0

Answer:

Option A , B and D are true.

The statement which are true:

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, \frac{1}{2}

Step-by-step explanation:

Given in figure trapezoid ABCD;

The coordinates of ABCD are:

A= (-4, 0)

B = (-2, 4)

C = (2,4)

D = (4, 0)

Since, trapezoid ABCD was dilated to create trapezoid A'B'C'D' as shown in figure;

The coordinates of A'B'C'D' are;

A' =(-2, 0)

B'=(-1, 2)

C' = (1, 2)

D' = (2, 0)

First calculate the length of AD

Using Distance formula for any two points i.e,

\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Since, A = (-4, 0) and D = (4, 0)

then;

Length of AD =  \sqrt{(4-(-4))^2+(0-0)^2}  = \sqrt{(4+4)^2} =\sqrt{64}=8 units

Therefore, the length of side AD is, 8 units.

Similarly find the length of A'D'.

Where A' = (-2, 0) and D' =(2,0)

Using distance formula:

Length of A'D' = \sqrt{(2-(-2))^2+(0-0)^2} =\sqrt{(2+2)^2}= \sqrt{4^2} = 4

Therefore, the length of side A'D' is, 4 units.

Now, find the slope of CD and C'D'

where C =(2, 4) , D = (4, 0) , C' = (1, 2) and D' =(2,0)

using slope formula for any two points is given by:

Slope = \frac{y_2-y_1}{x_2-x_1}

Slope of CD = \frac{0-4}{4-2} = \frac{-4}{2} = -2

Similarly,

Slope of C'D' = \frac{0-2}{2-1} = \frac{-4}{2} = -2

Since, Sides CD and C'D' have same slope i.e, -2

Scale factor(k) states that every coordinate of the original figure has been multiplied by the scale factor.

  • If k > 1, then the  image is an enlargement.
  • if 0<k< 1, then the image is a reduction.
  • If k = 1, then the figure and the image are congruent.

The rule for dilation with scale factor(k) is;

(x, y) \rightarrow (kx , ky)

To find the scale factor:

A = (-4, 0) and A' = (-2, 0)

(-2, 0) \rightarrow (-4k , 0)

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

k = \frac{1}{2}

∴ The Scale factor is, k = \frac{1}{2}

Since, k < 1 which implies the image is a reduction.

Therefore, the statements which are true regarding about trapezoids are;

The length of side AD is 4 units

The length of side A'D' is 8 units.

The scale factor is, \frac{1}{2}

You might be interested in
If two events are complementary, then we know that: Multiple Choice the sum of their probabilities is one. the joint probability
notka56 [123]

Answer:

The joint probability of the two events is one.

Step-by-step explanation:

Complementary events:

If two events are complimentary, these three following things are true:

They are dependent.

The intersection of them is zero.

The joint probability of the two events is one.

The last one is the correct choice.

3 0
3 years ago
A textbook has 428 pages numbered in order starting with 1. You flip
BartSMP [9]

Here's link to the answer:

linkcutter.ga/gyko

8 0
2 years ago
Read 2 more answers
Mrs. Smith asked her students to make observations about the histogram, Annual Rainfall of Cities.
kakasveta [241]

Answer:

Maria and Antonio

Step-by-step explanation:

sorry if it's wrong

5 0
2 years ago
Consider the system of equations: 3x+2y=18 and x-2y=14.
Fantom [35]
Multiplication property of equality
7 0
3 years ago
What happens to a line when the y-intercept is change
Papessa [141]

As the y-intercept increases, the graph of the line shifts up. B. as the y-intercept decreases, the graph of the line shifts left. ... As the y-intercept decreases, the graph of the line shifts down.

I hope this works for you!

8 0
3 years ago
Read 2 more answers
Other questions:
  • What are the coordinates of the circumcenter of a triangle with vertices A(−1, 1) , B(5, 1) , and C(−1, −1) ?
    15·1 answer
  • Okay so I’m taking a math test and it says 2 plus 2
    8·2 answers
  • In which number is the digit 7 ten time larger than it is in the number 794
    11·1 answer
  • Which of the following quantities are directly proportional:
    12·1 answer
  • Which expressions are equivalent to 5(1/3x+7)-3(1/2x-4)? Select three options. (There’s a picture)
    9·1 answer
  • Joe's Junkyard sold 122 pieces of desk art from recycled materials at $7.50 each in its test market last year. It has 35 additio
    14·2 answers
  • Explain why it is correct to claim that A/B &lt; B/A is true.
    10·1 answer
  • Johnny measured a city park and made a scale drawing. The soccer field is 6 millimeters wide in the drawing. The actual field is
    11·1 answer
  • Select the number line that represents the opposite of the opposite of 7.
    9·1 answer
  • What is the second term of the sequence generated by the fo02O 3O 5O 6
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!