Geometry Dilations Similarity Test – Free PDF

Contents

This geometry dilations similarity test checks dilations and similarity transformations in 45 minutes, with 9 questions for a total of 20 points.

This 45-minute test covers dilations and similarity transformations (G-SRT.A.1 to A.3). It includes scale factors, dilations on the coordinate plane, a similarity sequence and the AA criterion. Write each image point and show your reasoning. The test is worth 20 points.

Test information

Grade: Geometry
Chapter: Dilations and Similarity Transformations
Common Core: G-SRT.A.1, G-SRT.A.2, G-SRT.A.3
Time: 45 minutes
Total: 20 points (Question 1: 2 pts; Question 2: 2 pts; Question 3: 3 pts; Question 4: 2 pts; Question 5: 2 pts; Question 6: 3 pts; Question 7: 3 pts; Question 8: 2 pts; Question 9: 1 pt)

Geometry Dilations Similarity Test: questions 1–5

Question 1: Scale factor and image lengths (2 points)

A dilation with center O maps A to \(A^{\prime}\) and B to \(B^{\prime}\). In the figure, \(OA=5\) cm, \(OA^{\prime}=12.5\) cm, \(OB=4\) cm and \(AB=3\) cm.

Find the scale factor. (1 point)
Find \(A^{\prime}B^{\prime}\). (1 point)

A dilation with center O maps A to A′ and B to B′.

Question 2: Dilate points about the origin (2 points)

Dilate each point about the origin with the given scale factor and write the image.

\(P(4,-6),\ k=\frac{3}{2}\) (1 point)
\(Q(-10,15),\ k=0.4\) (1 point)

Question 3: Dilate a triangle on the plane (3 points)

Triangle ABC is graphed. It is dilated about the origin with scale factor 2 to form \(A^{\prime}B^{\prime}C^{\prime}\).

Find the coordinates of the three image vertices. (1 point)
Find \(BC\) and \(B^{\prime}C^{\prime}\). (1 point)
Show that \(BC\) and \(B^{\prime}C^{\prime}\) are parallel. (1 point)

Triangle ABC on the coordinate plane.

Question 4: Dilating a line (2 points)

Both lines are dilated about the origin with scale factor 4. Write an equation of each image.

\(y=-2x+3\) (1 point)
\(y=3x\) (1 point)

Question 5: Center other than the origin (2 points)

A dilation has center \(C(2,1)\) and scale factor 3. Find the image of each point.

\(A(4,3)\) (1 point)
\(B(-1,0)\) (1 point)

Geometry Dilations Similarity Test: questions 6–9

Question 6: Describe a similarity transformation (3 points)

Triangle DEF is the image of triangle ABC under a sequence of transformations.

Find the scale factor relating \(DE\) to \(AB\). (1 point)
Describe a sequence of a dilation and a rigid motion that maps ABC onto DEF. (1 point)
Use your sequence to show where C goes. (1 point)

Triangles ABC and DEF on the coordinate plane.

Question 7: AA similarity and a missing side (3 points)

Use the figure.

Find \(m\angle C\) and \(m\angle D\). (1 point)
Are the triangles similar? Name the criterion and write a similarity statement. (1 point)
Find \(EF\). (1 point)

Triangles ABC and DEF.

Question 8: Poster dilation (2 points)

Sofia enlarges a 5 inch by 7 inch photo into a poster that is 30 inches wide.

Find the scale factor and the height the poster needs for it to be a dilation of the photo. (1 point)
The print shop delivers a poster that is 30 inches by 40 inches. Is it a dilation of the photo? Explain. (1 point)