Use the image to answer the question.

Question

An illustration shows 2 trapezoids labeled Figure 1 and Figure 2 placed on a 12 column by 6 row grid. Figure 2 is smaller and a mirror image of Figure 1. Figure 1 shows the top left vertex on the top of the 3rd row and the start of the 3rd column, the top right vertex is on the top of the 3rd row and the start of the 5th column, the bottom left vertex is on the bottom of the 4th row and the start of 3rd column, and the bottom right vertex is on the bottom of the 4th row and the end of the 5th column. Figure 2 shows the top left vertex on the middle of the 3rd row and the middle of the 9th column, the top right vertex on the middle of the 3rd row and the end of the 10th column, the bottom left vertex on the end of the 4th row and on the 8th column, and the bottom right vertex on the end of the 4th row and end of the 10th column.

Describe the sequence of transformations that exhibits the similarity between Figures 1 and 2.

A. rotation and dilation

B. reflection and translation

C. translation and dilation

D. dilation and reflection

Answer 1

D. dilation and reflection

Answer 2

Use the image to answer the question.

A rectangle split into four separate and equal boxes shows four illustrations with corresponding labels as follows: Figure 1: chair; figure 2: tree; figure 3: nut; and figure 4: house.

Which scale drawing is a dilation that increased the size of the original object it represents?

Answer 3

To accurately determine which scale drawing represents a dilation that increased the size of the original object, we would need further information or visual reference to compare the sizes of the original and scaled drawings. Without this information, it is not possible to determine the correct answer.

Answer 4

If you would like to dilate a square with a side length of 8 units to create a square with a side length of 20 units, what scale factor should you use? Write your answer in decimal form.

Answer 5

To find the scale factor, we can divide the length of the new square by the length of the original square:

Scale factor = Length of new square / Length of original square

Scale factor = 20 / 8 = 2.5

Therefore, the scale factor should be 2.5.

Answer 6

You use scale factor of 34 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?

Answer 7

To find the radius of the original circle, we need to divide the radius of the dilated circle by the scale factor:

Radius of original circle = Radius of dilated circle / Scale factor

Radius of original circle = 9 inches / 34

Radius of original circle ≈ 0.2647 inches (rounded to four decimal places)

Answer 8

You use scale factor of 3/4 to create a dilated circle with a radius of 9 inches. What is the radius of the original circle?

Answer 9

To find the radius of the original circle, we need to divide the radius of the dilated circle by the scale factor:

Radius of original circle = Radius of dilated circle / Scale factor

Radius of original circle = 9 inches / (3/4)

Using the reciprocal of a fraction, which is the same as multiplying by its inverse, we can rewrite the equation as:

Radius of original circle = 9 inches * (4/3)

Simplifying the expression:

Radius of original circle = 36 inches / 3

Radius of original circle = 12 inches

Therefore, the radius of the original circle is 12 inches.

Answer 10

Use the image to answer the question.

An illustration shows two triangles, one big and one small. In the small triangle, one side measures 11.4 inches and another side measures 18 inches. In the big triangle, the side corresponding to 11.4 inches in the small triangle measures x and the side corresponding to 18 inches measures 23.4 inches.

What is the length of x in decimal form to the nearest hundredth?

Answer 11

To find the length of x, we can set up a proportion using the corresponding sides of the two triangles:

Small triangle:
Side 1: 11.4 inches
Side 2: 18 inches

Big triangle:
Side 1: x inches
Side 2: 23.4 inches

We can set up the proportion:

11.4 inches / 18 inches = x inches / 23.4 inches

To find the value of x, we can cross multiply and solve for x:

11.4 inches * 23.4 inches = 18 inches * x inches

266.76 = 18x

Divide both sides of the equation by 18:

x = 14.82 inches

Therefore, the length of x is equal to 14.82 inches to the nearest hundredth.