Question 1

Three congruent figures are shown in the coordinate plane.

Which statement describes a possible sequence of transformations that transforms figure $1$ into figure $2$?

Accepted Answer

a reflection across the $x-	ext{axis}$, followed by a translation $3$ units to the right

Answer

a rotation $180^\circ$ clockwise about the origin, followed by a translation $2$ units to the left

Answer

a rotation $180^\circ$ clockwise about the origin, followed by a translation $3$ units to the right

Answer

a reflection across the $x-	ext{axis}$, followed by a translation $2$ units to the left

Question 2

Three congruent figures are shown in the coordinate plane.

Figure $3$ can also be created by transforming figure $1$ with a sequence of two transformations.

Which statement describes a possible sequence of transformations that transforms figure $1$ into figure $3$?

Accepted Answer

a rotation $90^\circ$ clockwise about the origin, followed by a reflection across the $x-	ext{axis}$

Answer

a rotation $180^\circ$ clockwise about the origin, followed by a reflection across the $y-	ext{axis}$

Answer

a rotation $90^\circ$ clockwise about the origin, followed by a translation $3$ units to the right

Answer

a rotation $180^\circ$ clockwise about the origin, followed by a translation $2$ units to the left

Question 3

The figure shows a right-circular cylinder and a right-circular cone. The cylinder and the cone have the same base and the same height.

What is the volume, in cubic feet, of the cone?

Accepted Answer

$16\pi$

Answer

$36\pi$

Answer

$12\pi$

Answer

$48\pi$

Question 4

The figure shows a right-circular cylinder and a right-circular cone. The cylinder and the cone have the same base and the same height.

What is the ratio of the cone's volume to the cylinder's volume?

Accepted Answer

$\frac{1}{3}$

Answer

$\frac{1}{4}$

Answer

$\frac{1}{2}$

Answer

$\frac{1}{1}$

Question 5

In $\vartriangle{ABC},\,\overline{BD}$ is perpendicular to $\overline{AC}$. The dimensions are shown in centimeters.

What is the length, in centimeters, of $\overline{AC}$?
Enter your answer in the box.

Accepted Answer

12

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