Question 1

On the set of axes below, $\bigtriangleup AB'C'$ is the image of $\bigtriangleup ABC$ .

What is the scale factor and center of dilation that maps $\bigtriangleup ABC$ onto $\bigtriangleup AB'C'$ ?

Accepted Answer

$2$ and vertex $A$

Answer

$2$ and the origin

Answer

$2$ and vertex $A$

Answer

$2$ and the origin

Question 2

Line segment $\bigtriangleup AB'C'$ has endpoints whose coordinates are $\bigtriangleup ABC$ and $Q(3,-4)$ .

What are the coordinates of point $\bigtriangleup AB'C'$ , such that $PA:AQ=2:3$ ?

Accepted Answer

Answer

Answer

Answer

Question 3

On the set of axes below, congruent parallelograms $\bigtriangleup AB'C'$ and $\bigtriangleup ABC$ are graphed.

Which sequence of transformations maps $\bigtriangleup ABC$ onto $\bigtriangleup AB'C'$ ?

Accepted Answer

a translation four units down followed by a reflection over the y-axis

Answer

a translation ten units to the left followed by a reflection over the x-axis

Answer

a reflection over the y-axis followed by a translation of two units down

Answer

a reflection over the x-axis followed by a translation ten units to the left and one unit up

Question 4

Triangle $\bigtriangleup AB'C'$ has a right angle at $\bigtriangleup ABC$ . If $Q(3,-4)$ and $m\angle B=24°$ , what is $AB$ , to the nearest tenth?

Accepted Answer

Answer

Answer

Answer

Question 5

Given $\bigtriangleup AB'C'$ and $\bigtriangleup ABC$ with $Q(3,-4)$ , which additional statement is sufficient to always prove $m\angle B=24°$ ?

Accepted Answer

$2$ and $A$

Answer

$2$ and $A$

Answer

$2$ and $A$

Answer

$2$ and $A$

Question 6

The equation of a circle is $\bigtriangleup AB'C'$ .

What are the coordinates of the center and the length of the radius?

Accepted Answer

center $\bigtriangleup AB'C'$ and radius $\bigtriangleup ABC$

Answer

center $\bigtriangleup AB'C'$ and radius $\bigtriangleup ABC$

Answer

center $\bigtriangleup AB'C'$ and radius $\bigtriangleup ABC$

Answer

center $\bigtriangleup AB'C'$ and radius $\bigtriangleup ABC$

Question 7

A square with a side length of $\bigtriangleup AB'C'$ is continuously rotated about one of its sides. The resulting three-dimensional object is a

Accepted Answer

cylinder with a volume of $\bigtriangleup AB'C'$ .

Answer

cube with a volume of $\bigtriangleup AB'C'$ .

Answer

cylinder with a volume of $\bigtriangleup AB'C'$ .

Answer

cube with a volume of $\bigtriangleup AB'C'$ .

Question 8

Line $\bigtriangleup AB'C'$ is represented by the equation $\bigtriangleup ABC$ .

Which equation represents a line that is perpendicular to line $\bigtriangleup ABC$ and passes through the point $\bigtriangleup AB'C'$ ?

Accepted Answer

<math>y-2=-\frac{4}{7}\left(x+5\right)</math>

Answer

<math>y+2=\frac{4}{7}\left(x-5\right)</math>

Answer

<math>y+2=-\frac{4}{7}\left(x-5\right)</math>

Answer

<math>y-2=\frac{4}{7}\left(x+5\right)</math>

Question 9

Scalene triangle $\bigtriangleup AB'C'$ is drawn below.

If median $\overline{\mathrm{LM}}$ is drawn to side $\bigtriangleup ABC$ , which statement is always true?

Accepted Answer

Answer

<math>\overline{\mathrm{LM}}\perp\overline{\mathrm{KJ}}</math>

Answer

<math>\angle KLM\cong\angle JLM</math>

Answer

Question 10

In circle $\bigtriangleup AB'C'$ , chord $\bigtriangleup ABC$ intersects diameter $Q(3,-4)$ at $m\angle B=24°$ .

If $PA:AQ=2:3$ and $m\overset{\large\frown}{YA}=105\degree$ , what is $m\angle ASN$ ?

Accepted Answer

<math>97.5\degree</math>

Answer

<math>75\degree</math>

Answer

<math>120\degree</math>

Answer

<math>22.5\degree</math>

Question 11

Triangle $\bigtriangleup AB'C'$ is graphed on the set of axes below. The vertices of $\bigtriangleup ABC$ have coordinates $Q(3,-4)$ , $m\angle B=24°$ , and $AB$ .

What is the area of $m\overset{\large\frown}{YA}=105\degree$ ?

Accepted Answer

Answer

Answer

Answer

Question 12

In $\bigtriangleup AB'C'$ below, $\bigtriangleup ABC$ is a midsegment, and $Q(3,-4)$ .

Which statement is always true?

Accepted Answer

$2$ is isosceles

Answer

$2$ is scalene

Answer

<math>\overline{\mathrm{BD}}\ \cong\ \overline{\mathrm{BE}}</math>

Answer

<math>\overline{\mathrm{DA}}\ \cong\ \overline{\mathrm{E}}C</math>

Question 13

As shown in the diagram below, $\bigtriangleup AB'C'$ , $\bigtriangleup ABC$ , and $Q(3,-4)$ .

If $\bigtriangleup AB'C'$ , what is $PA:AQ=2:3$ ?

Accepted Answer

Answer

Answer

Answer

Question 14

The ratio of similarity of square $\bigtriangleup AB'C'$ to square $\bigtriangleup ABC$ is $Q(3,-4)$ . If $m\angle B=24°$ and $AB$ , then the perimeter of $ABCD$ is

Accepted Answer

Answer

Answer

Answer

Question 15

In parallelogram $\bigtriangleup AB'C'$ below, diagonals $\bigtriangleup ABC$ and $Q(3,-4)$ intersect at $m\angle B=24°$ .

Which transformation would map $PA:AQ=2:3$ onto $m\overset{\large\frown}{YA}=105\degree$ ?

Accepted Answer

a clockwise rotation of $\bigtriangleup AB'C'$ about point $\bigtriangleup ABC$

Answer

a reflection over $\bigtriangleup AB'C'$

Answer

a clockwise rotation of $\bigtriangleup AB'C'$ about point $\bigtriangleup ABC$

Answer

a reflection over $\bigtriangleup AB'C'$

Question 16

The square pyramid drawn below has a volume of $\bigtriangleup AB'C'$ .

If the height of the pyramid is $\overline{\mathrm{LM}}$ , what is the perimeter of the base?

Accepted Answer

Answer

Answer

Answer

Question 17

A glass fish tank is designed to be placed on a stand in the corner of a room with perpendicular walls. The tank can be modeled using part of a cylinder, as shown below. The inner length of the fish tank along the wall is $\bigtriangleup AB'C'$ inches, and the height of the tank is $\bigtriangleup ABC$ inches.

How much water, to the nearest gallon, does the fish tank hold?

$AB$

Accepted Answer

Answer

Answer

Answer

Question 18

Line $\bigtriangleup AB'C'$ , whose equation is $\bigtriangleup ABC$ , is dilated by a scale factor of $Q(3,-4)$ centered at the origin. Which equation represents the image of line $m\angle B=24°$ ?

Accepted Answer

Answer

Answer

Answer

Question 19

In right triangle $\bigtriangleup AB'C'$ below, altitude $\bigtriangleup ABC$ is drawn to hypotenuse $Q(3,-4)$ .

Which statement is always true?

Accepted Answer

Answer

Answer

Answer

Question 20

What is the measure, in radians, of a central angle that intercepts an arc length of $\bigtriangleup AB'C'$ cm in a circle with a diameter of $\bigtriangleup ABC$

Accepted Answer

Answer

Answer

Answer

Question 21

A regular nonagon has a center point, $\bigtriangleup AB'C'$ What degree of rotation about point $\bigtriangleup ABC$ will carry the nonagon onto itself?

Accepted Answer

Answer

Answer

Answer

Question 22

If two sides of a triangle have lengths of $\bigtriangleup AB'C'$ and $\bigtriangleup ABC$ , the length of the third side could be

Accepted Answer

Answer

Answer

Answer

Question 23

The car tire shown in the photograph below has a diameter of $\bigtriangleup AB'C'$ feet.

Approximately how many rotations will the tire make in one mile?

Accepted Answer

Answer

Answer

Answer

Question 24

In quadrilateral $\bigtriangleup AB'C'$ , $\bigtriangleup ABC$ and $Q(3,-4)$ .

Which additional information is sufficient to prove quadrilateral $\bigtriangleup AB'C'$ is a rhombus?

Accepted Answer

<math>\overline{\mathrm{ON}}\perp\overline{\mathrm{TW}}</math>

Answer

$2$ and $A$ bisect each other.

Answer

<math>\overline{\mathrm{TO}}\perp\overline{\mathrm{OW}}</math>

Answer

<math>\overline{\mathrm{OW}}\parallel\overline{\mathrm{TN}}</math>

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