8.3B Questions 1-10

A square has a perimeter of 160 centimeters. If the square is dilated with a scale factor of 0.9, what is the length of each side of the dilated square in centimeters?

Record your answer on the space below. Make sure to use the correct place value.

Quadrilateral  $FGHI$  has coordinates  $F\left(0,\ -4\right),\ G\left(-3,\ 4\right),\ H\left(4,\ 7\right),\$  and  $I\left(9,0\right)$  . Quadrilateral  $FGHI$  is dilated with a scale factor of 1.5 using the origin as the center of dilation. Which of the following could be a vertex of the dilated quadrilateral?

• F     (0, -5)

• G     (-4.5, 7)

• H     (6, 10.5)

• J     (13, 0)

Triangle $ABC$ has vertices  $A\left(5,\ 7\right),\ B\left(-4,\ 2\ \right),\$  and  $C\left(2,\ 0\right)$  . Which statement is true after dilating the triangle by a scale factor of 3 with the origin as the center of dilation?  

• A     The ratio of the  $x-$  coordinates of corresponding vertices of the dilated triangle to the original triangle is 3. 

• B     The coordinates of $A'$ is  $\left(8,\ 10\right)$  . 

• C     The distance from the origin to  $A$  is three times the distance from the origin to  $A'.$  

• D     The ratio of the  $y-$  coordinates of vertices of the dilated triangle to the  $y-$  coordinates of the corresponding vertices original triangle is  $\frac{1}{3}.$  

Which of the following statements is NOT true for figures and their dilation when the origin is the center of dilation?

• F Corresponding sides of the dilated figure and the original figure are proportional.

• G Corresponding angles of the dilated figures and the original figures are congruent.

• H The corresponding coordinates of the vertices of the image are the coordinates of the preimage multiplied by a scale factor.

• J If the scale factor for the dilation of the figure is 0.9, then the dilation is an enlargement.

In the figure below,  $\Delta A'BC'\$  is the dilation of  $\Delta ABC.$  The vertices of  $\Delta ABC$  are  $A\left(-4,\ 3\right),\ B\left(0,\ 0\right)$  and  $C\left(-4,\ 0\right).$  

Which proportion is true? 

• A      $\frac{A'C'}{3}=\frac{AB}{A'B}$  

• B      $\frac{BC'}{4}=\frac{A'C'}{3}$  

• C      $\frac{BC'}{4}=\frac{A'B'}{3}$  

• D      $\frac{AB}{A'B}=\frac{3}{4}$  

A rhombus has a perimeter of 40 centimeters. If the rhombus is dilated with a scale factor of 1.5, what is the length of each side of the image in centimeters?

Record your answer on the space below. Be sure to sure the correct place value.

Rectangle $A'B'C'D'$ is a dilation of rectangle  $ABCD$  using the origin as the center of dilation. It is graphed on the coordinate grid.  

Which statement is true about the coordinates of  $B'?$  

• A      $B'\left(-3,\ -2.5\right)$  because the ratio of the  $y-$  coordinates of  $B'$  and  $B$  is  $\frac{1}{2}.$  

• B      $B'\left(-3,\ -3\right)$  because the ratio of the  $y-$  coordinates of  $B'$  and  $B$  is  $\frac{4}{5}.$  

• C      $B'\left(-3,\ -2\right)$  because the ratio of the  $x-$  coordinates of  $B'$  and  $B$  is  $\frac{2}{3}.$  

• D      $B'\left(-3,\ -2\ \frac{1}{3}\right)$  because the ratio of the  $x-$  coordinates of  $B'$  and  $B$  is  $\frac{1}{3}.$  

If $\Delta RST$  is dilated to form  $\Delta R'S'T'$  and the dilation is a reduction, which of the following could NOT be a true statement? 

• F      $\frac{R'S'}{RS}=\frac{1}{3}$  

• G      $\frac{R'T'}{RT}=\frac{5}{8}$  

• H      $\frac{S'T'}{ST}=\frac{2}{3}$  

• J      $\frac{R'T'}{RT}=\frac{3}{2}$  

If $\Delta RST$ is dilated to form  $\Delta R'S'T'$  and the dilation is an enlargement, which of the following could be a true statement?  

• A      $\frac{R'S'}{RS}=\frac{1}{3}$  

• B      $\frac{R'T'}{RT}=\frac{5}{2}$  

• C      $\frac{S'T'}{ST}=\frac{9}{12}$  

• D      $\frac{R'T'}{RT}=\frac{3}{7}$  

 $\Delta RST$  is dilated to form  $\Delta R'S'T'\$  with a scale factor of 12. If  $RS=4,$  what is the length of  $\overline{R'S'?}$  

• F     16

• G     3

• H     48

• J        8