Trapezoid abcd was dilated to create trapezoid a'b'c'd'. which statements are true about the trapezoids? check all 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 .

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,

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,

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

then;

Length of AD =   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' =

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:

Similarly,

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.

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

To find the scale factor:

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

On comparing we ghet;

-4k = -2

Divide -4 both sides we get;

∴ The Scale factor is,

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,

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