Mathematics, 11.09.2019 17:20 mucciak9414

Trapezoid abcd was dilated to create trapezoid a'b'c'd'. on a coordinate plane, 2 trapezoids are shown. trapezoid a b c d has points (negative 4, 0), (negative 2, 4), (2, 4) and (4, 0). trapezoid a prime b prime c prime d prime has points (negative 2, 0), (negative 1, 2), (1, 2), and (2, 0). which statements are true about the trapezoids? select three options. 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 1/2.

Answers: 1

Show answers

Answers

Answer from: Arealbot

The true statements are:

(A) The length of side AD is 8 unit.

(B) The length of side A'D' is 4 unit.

(D) Sides CD and C'D' both have same slope.

(E) The scale factor is (1/2).

Step-by-step explanation:

Given information:

A(-4,0), B(-2,-4),C(2,4),D(4,0)

A'(-2,0),B'(-1,2),C'(1,2),D'(2,0)

As, we know:

When two figures are similar then the ratio of their sides is proportional and that ratio is called the scale factor.

(A) The length of side AD is 8 unit.

we have:

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

on substituting the values in above formula:

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

Hence, the statement is true .

(B)The length of side A'D' is 4 unit.

we have:

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

on substituting the values in above formula:

$A'D'=\sqrt{(0-0)^2+(2+2)^2}\\A'D'=\sqrt{8} \\A'D'=4$

Hence, the statement is true .

(C)The image is larger than the pre-image.

We have

The pre-image is the trapezoid ABCD

The image is the trapezoid A'B'C'D'

Now the scale factor:

A'D'/AD=4/8

A'D'/AD=0.5

Hence , the image is smaller then the pre-image so the statement is false.

(D)Sides CD and C'D' both have same slope

Now , the slope between two point is calculated as

$m=\frac{y_2-y_1}{x_2-x_1} \\$

On putting the values :

Slope of CD

$m=\frac{0-4}{4-2} \\m=-2$

And similarly

Slope of C'D'

$m=\frac{0-2}{2-1} \\m=-2\\$

Hence the statement is true, The slope of CD and C'D' is same.

(E)The scale factor is (1/2)

The scale factor is the ratio between the corresponding sides

So,

A'D'/AD=4/8

A'D'/AD=1/2

Hence the statement is true , The scale factor is (1/2)

For more information visit:

link

Answer from: lovenahofer

The length of side AD is 8 units.

The length of side A'D' is 4 units

Sides CD and C'D' both have the same slope

The scale factor is 1/2

Step-by-step explanation:

we have

A(-4,0),B(-2,4),C(2,4),D(4,0)

A'(-2,0),B'(-1,2),C'(1,2),D'(2,0)

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

Verify each statement

Part 1) The length of side AD is 8 units.

The statement is true

because, the formula to calculate the distance between two points is $d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A(-4,0),D(4,0)

substitute the values

$AD=\sqrt{(0-0)^{2}+(4+4)^{2}}$

$AD=\sqrt{(0)^{2}+(8)^{2}}$

$AD=8\ units$

Part 2) The length of side A'D' is 4 units

The statement is true

because, the formula to calculate the distance between two points is $d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

A'(-2,0),D'(2,0)

substitute the values

$A'D'=\sqrt{(0-0)^{2}+(2+2)^{2}}$

$A'D'=\sqrt{(0)^{2}+(4)^{2}}$

$A'D'=4\ units$

Part 3) The image is larger than the pre-image

The statement is false

Because

The pre-image is the trapezoid ABCD

The image is the trapezoid A'B'C'D'

Find out the scale factor

The scale factor is the ratio between corresponding sides

A'D'/AD=4/8=0.5

The scale factor is 0.5

therefore

The image is smaller than the pre-image

Part 4) Sides CD and C'D' both have the same slope

The statement is true

Because, the dilation does not change the shape of the figure

Verify

Find the slope CD

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

C(2,4),D(4,0)

substitute

$mCD=\frac{0-4}{4-2}$

$mCD=\frac{-4}{2}=-2$

Find the slope C'D'

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

C'(1,2),D'(2,0)

substitute

$mC'D'=\frac{0-2}{2-1}$

$mC'D'=\frac{-2}{1}=-2$

mCD=mC'D' -----> is verified

Part 5) The scale factor is 1/2

The statement is True

Because

The scale factor is the ratio between corresponding sides

A'D'/AD=4/8=1/2

The scale factor is 1/2

The scale factor is less than zero, so the dilation is a reduction

Answer from: Quest

What are the options

Answer from: Quest

I’d say letter a..
Which complex number is represented by the pointe graft on the complex plane below? a. -4+3i b. 3+4

Another question on Mathematics

Mathematics, 21.06.2019 18:30

At the olympic games, many events have several rounds of competition. one of these events is the men's 100-meter backstroke. the upper dot plot shows the times (in seconds) of the top 8 finishers in the final round of the 2012 olympics. the lower dot plot shows the times of the same 8 swimmers, but in the semifinal round. which pieces of information can be gathered from these dot plots? (remember that lower swim times are faster.) choose all answers that apply: a: the swimmers had faster times on average in the final round. b: the times in the final round vary noticeably more than the times in the semifinal round. c: none of the above.

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

Consider this expression and the steps to evaluate it. 4^5(−2)^9/4^8(−2)^3 1. apply the quotient of powers: (−2)^a/4^b 2. evaluate powers: c/d select the value of each variable. a = _ b = _ c = _ d = _

Answers: 3

Answer

Mathematics, 22.06.2019 04:00

Sean is his dad build a tiled walkway in their backyard. the walkway will be 6060 feet long and 22 feet wide. the local hardware store sells tiles which are 22 by 22 feet and come in boxes of 66. how many boxes of tiles do they need?

Answers: 1

Answer

Mathematics, 22.06.2019 05:00

Sal is making bracelets for a fundraiser. he uses 6 inches of yarn per bracelet . how many bracelets can sal make with 5 feet of yarn

Answers: 1

Answer

You know the right answer?

Trapezoid abcd was dilated to create trapezoid a'b'c'd'. on a coordinate plane, 2 trapezoids are sho...

Questions