Dilations & Similarity Practice Test

Given that  $\Delta ABC\sim\Delta FED$ , find the value of x. 

• x = 9

• x = 3.9

• x = - 0.26

• x = 9.95

Tags

CCSS.HSG.SRT.A.2

Let  $\Delta XYZ$ be the dilated image of  $\Delta ABC$ with a scale factor of k = 3. Which of the following is the correct center of dilation?

• (0, 0)

• (4, 1)

• (-5, 5)

• (1, 4)

Tags

CCSS.8.G.A.3

Which of the following must be true in order for  $\Delta BCD\sim\Delta RST$ ? 

• a = 12 b = 8

• a = 24 b = 16

• a = 6, b = 4

• a = 11, b = 13

Tags

CCSS.HSG.SRT.A.2

Let triangle EFG be a mapped image, dilated about the origin, from triangle JKL with a scale factor k=4 with J(2,2), K(3,4), L(1,0). Which of the following are the coordinates for E?

• (12, 16)

• (8, 8)

• (4, 4)

• (4, 0)

Tags

CCSS.8.G.A.3

Let $\Delta A'B'C'$ be a dilation of   $\Delta ABC$  with a scale factor of k= 1/2 and a center of dilation at (-4,1). Which of the following coordinates are vertices of  $\Delta A'B'C'$   ? [Circle all that apply.]

• (-3, 2)

• (-2, 3)

• (-0.5, 0.5)

• (-2, 0.5) (-0.5, 0.5)

• (-2, -1)

Tags

CCSS.8.G.A.3

Given that  $\Delta MNL$ and  $\Delta UVL$  are similar, solve for x. 

• x = -14

• x = -9

• x = -19.67

• x = 7

Tags

CCSS.HSG.SRT.A.2

Mr. Murphy designed a new logo for the NHS math team. Part of the logo includes a pair of similar triangles as shown in the figure below.

• The center of dilation for these triangles must be one of the vertices of the outside triangle.

• The center of dilation for these triangles must be one of the vertices of the inside triangle.

• The center of dilation for these triangles must be in the interior of the two triangles.

• The center of dilation for these triangles must be exterior to the two triangles.

Tags

CCSS.8.G.A.4

CCSS.HSG.SRT.A.2

Given $\Delta ABC$ is a dilated image of  $\Delta JKL$ with a scale factor of 4, which of the following proportions are true? Select all that apply. 

•  $\frac{AB}{JK}=\frac{BC}{KL}$  

•  $\frac{AC}{JK}=\frac{BC}{KL}$  

•  $\frac{BC}{KL}=4$  

•  $\frac{KL}{BC}=4$  

•  $\frac{JL}{AC}=\frac{AB}{JK}$  

Tags

CCSS.7.G.A.1

Let $\Delta DEF$ be dilated by a scale factor of ½ to form the image  $\Delta RST$ . Let RS be 12 inches long. How long is DE? 

• 12 inches

• 24 inches  

• 6 inches

• The length of DE cannot be determined.

Tags

CCSS.8.G.A.3

If line segment AB is dilated about center P by a scale factor of ½ to form A’B’, which statement(s) is/are true? Choose all that apply. 

• AB and A’B’ are parallel. 

• A’B’ is twice as long as AB. 

•  $\angle ABP\cong\angle BAP$ because they are corresponding angles on parallel lines. 

•  $\frac{AP}{A'P}=\frac{1}{2}$  

• The endpoints of A’B’ are ½ the distance to P as the endpoints of AB. 

Tags

CCSS.8.G.A.3