Question

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.

Answer 1

Answer:

a,b,d and e

Step-by-step explanation:

Answer 2

Answer:

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

so

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

so

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