Transformations and Area Relationships

Triangle RST is rotated 270° counterclockwise about the origin of a coordinate plane to create triangle R'S'T'. Which rule describes this transformation?

• (x, y) → (x, -y)

• (x, y) → (-x, y)

• (x, y) → (-y, x)

• (x, y) → (y, -x)

A transformation is applied to a figure to create a new figure. Which transformation does NOT preserve congruence?

• A reflection across the x-axis

• A translation 7 units down

• A dilation by a scale factor of 5

• A rotation of 90° clockwise

A sphere has a diameter of 11 centimeters.

Which measurement is closest to the volume of the sphere in cubic centimeters.

• 1774.7π

• 696.9π

• 5575.9π

• 221.8π

Amanda's favorite snack can be modeled as a hemisphere sitting on a cone.

Which measurement is closest to the volume of the snack container in cubic centimeters?

• 2,661 cm³

• 10,010 cm³

• 5,195 cm³

• 7,983 cm³

Triangle TRW is shown on the coordinate grid.

Triangle TRW will be dilated by a scale factor of n with the origin as the center of dilation to create triangle T'R'W'. Which ordered pair best represents the location of point R'?

• (- 3/n, - 5/n)

• (-3n, -5n)

• (-3 + n, -5 + n)

• (-3 - n, -5 - n)

The side lengths in yards of a triangle and a square are shown in the diagram.

The perimeter of the triangle is equal to the perimeter of the square. The equation can be used to find the value of x.

6x + 3 = 4x + 20

What is the value of x?

• x = -9

• x = 9

• x = -8.5

• x = 8.5

Natasha walked from her house to the library and then to the grocery store. The diagram shows the top view of the locations of these three places and their distances from each other.

Which measurement is closest to the shortest distance in miles from the grocery store to Natasha's house?

• 1. 1.2 mi

• 0.4 mi

• 0.8 mi

• 2.6 mi

A triangular prism and its dimensions in centimeters are shown.

What is the lateral surface area of the prism in square centimeters?

• 192 cm²

• 128 cm²

• 152 cm²

• 176 cm²

A house has a rectangular backyard patio that are similar shapes. Each dimension of the backyard is 3.2 times the corresponding dimension of the patio.

Which statements are true?

Select TWO correct answers

• The area of the backyard is 6.4 times the area of the patio.

• The area of the backyard is 10.24 times the area of the patio.

• The area of the backyard is 3.2 times the area of the patio.

• The perimeter of the backyard is 6.4 times the perimeter of the patio.

• The perimeter of the backyard is 3.2 times the perimeter of the patio.

The two lines graphed on the coordinate grid represent a system of equations.

What is the y-coordinate of the ordered pair that best represents a solution to both equations?

• 5

• -7

• 0

• 1/7