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.

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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)

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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

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Answer from: Quest

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