Category 3

Point M is located at (4, 6) on a coordinate grid. Point M is translated 8 units to the left and 9 units down to create point M′.

Which measurement is closest to the distance between point M and point M′ in units?

• 4 units

• 17 units

• 9 units

• 12 units

In the diagram a person who is 6 ft tall is standing on the ground 3 ft away from point P. A line segment drawn from the top corner of the building to point P creates two similar triangles.

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The coordinate grid shows parallelogram PQRS.

Parallelogram PQRS is rotated 90° clockwise about the origin to create parallelogram P'Q'R'S' . Which rule describes this transformation?

• ( x, y) --> (x, -y)

• ( x, y) --> (-x, y)

• ( x, y) --> (y, x)

• ( x, y) --> (y, -x)

A preschool has a rectangular field and a rectangular playground that are similar in shape. Each dimension of the field is 3.2 times the corresponding dimension of the playground. Which statement is true?

• The area of the field is 6.4 times the area of the playground.

• The area of the field is 10.24 times the area of the playground.

• The perimeter of the field is 6.4 times the perimeter of the playground.

• The perimeter of the field is 10.24 times the perimeter of the playground.

A ball shaped like a sphere has a radius of 2.7 centimeters. Which measurement is closest to the volume of the ball in cubic centimeters?

• 46.38 cm³

• 33.93 cm³

• 122.15 cm³

• 82.45 cm³

The coordinates of the vertices of a quadrilateral are P (1, 2), R (1, 4), S (3, 4), and T (4, 2).

Quadrilateral PRST is reflected across the y-axis to create quadrilateral P'R'S'T'. Which rule describes this transformation?

• (x, y) -> (x, -y)

• (x, y) -> (-x, y)

• (x, y) -> (y, -x)

• (x, y) -> (-y, x)

Four triangles are shown.

Based on these triangles, which statement is true?

• w = 75°, because 45 + 60 = 105 and 180 - 105 = 75

• w = 105°, because 180 - (45 + 60) = 75 and 180 - 75 = 105

• w = 285°, because 45 + 60 = 105 and 105 + 180 = 285

• w = 165°, because 180 - 60 = 120 and 120 + 45 = 165

The diagram below shows the side view of a ramp used to help load and unload a moving van.

Which measurement is closest to the length of the ramp in feet?

• 8.5 ft

• 10.5 ft

• 9.5 ft

• 13.5 ft

Which representation of a transformation on a coordinate grid does not preserve congruence?

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An artist joined three square regions at their vertices to create the figure shown in the diagram.

The artist will use small congruent square tiles to cover each region without any gaps or overlaps. Based on the information, which statement is true?

• The number of tiles needed to cover Region X is the same as the number of tiles needed to cover both Region Y and Region Z.

• The number of tiles needed to cover Region Y is the same as the number of tiles needed to cover both Region X and Region Z.

• The number of tiles needed to cover Region Z is the same as the number of tiles needed to cover both Region X and Region Y.

• None of these