-9c --12 +3c =12 what does c=

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

hichkok12 [17]

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, $\frac{1}{2}$

6 0

3 years ago

Hello, I'm new to homeschooling and I have a question. Do teachers approve of this answer??? I don't know what happens when I su

snow_lady [41]

Answer:my mom said yes shes my teacher

4 0

3 years ago

Read 2 more answers

Find the unit rate $72 in 4 hours

shepuryov [24]

Answer:

72 dollars ÷ 4

4 hours ÷ 4

=

18 dollars

1 hour

=

18 dollars

hour

= 18 dollars per hour

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

A wall with a height of 20 feet is braced with a support post that forms a 30 degree angle with the top of the wall. What is the

dexar [7]

The length of the support post is 40 ft.

<u>Solution:</u>

Given, the height of the wall is 20 ft; support post forms 30 degree

Refer the attached image

Let us name the triangle as ABC where AB is the wall (opposite side) of 20 ft and $\angle A$ is 30 degree ( $\theta$ ) and AC is the length of the post.

To find: The length of the post (AC)

we know the formula, $sin\theta=\frac{opp}{hyp}$ (trigonometric formula)

On substituting the values we get,

$\Rightarrow sin(30^{\circ})=\frac{20}{AC}$

The value of sin 30 degree is 0.5

$\Rightarrow 0.5=\frac{20}{AC}\rightarrow AC=\frac{20}{0.5}\rightarrow AC=40 ft$

3 0

3 years ago

Which best explains whether or not ABC = LMN?

Masja [62]

Answer:

If I've done it right the answer should be A, the figures are congruent because a 270 rotation about the origin a d a reflection of the x-axis

7 0

3 years ago